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Longer titles found: Permutation (Amon Tobin album) (view), Permutation (Bill Laswell album) (view), Permutation (disambiguation) (view), Permutation (music) (view), Permutation City (view), Permutation Patterns (conference) (view), Permutation automaton (view), Permutation box (view), Permutation category (view), Permutation class (view), Permutation code (view), Permutation graph (view), Permutation group (view), Permutation matrix (view), Permutation model (view), Permutation pattern (view), Permutation polynomial (view), Permutation representation (view), Permutation representation (disambiguation) (view), Permutation test (view), Permutational analysis of variance (view), Permutationally invariant quantum state tomography (view), Substitution–permutation network (view), Cyclic permutation (view), Parity of a permutation (view), Generalized permutation matrix (view), Circular permutation in proteins (view), Variably Modified Permutation Composition (view), The Platonic Permutation (view), Random permutation (view), Alternating permutation (view), The Isolation Permutation (view), List of permutation topics (view), Primitive permutation group (view), Pseudorandom permutation (view), Partial permutation (view), Random permutation statistics (view), Rank 3 permutation group (view), Bit-reversal permutation (view), Riffle shuffle permutation (view), Separable permutation (view), Enumerations of specific permutation classes (view), Skew and direct sums of permutations (view), Stirling permutation (view), Block (permutation group theory) (view), Superpermutation (view), Vexillary permutation (view), Stack-sortable permutation (view), Baxter permutation (view), Claw-free permutation (view), Programming by permutation (view), Place-permutation action (view), Skew-merged permutation (view), Layered permutation (view), Combinations and permutations (view)

searching for Permutation 113 found (2652 total)

alternate case: permutation

CFOP method (2,320 words) [view diff] exact match in snippet view article find links to article

its vertical edge at the same time. There are 42 unique cases for the permutations of a corner and its matching edge on the cube (one of which corresponds
Trapdoor function (1,316 words) [view diff] exact match in snippet view article find links to article
function in the collection above is a one-way permutation, then the collection is also called a trapdoor permutation. In the following two examples, we always
One-way function (1,956 words) [view diff] exact match in snippet view article find links to article
A one-way permutation is a one-way function that is also a permutation—that is, a one-way function that is bijective. One-way permutations are an important
Optimal asymmetric encryption padding (1,460 words) [view diff] exact match in snippet view article find links to article
asymmetric encryption. When combined with any secure trapdoor one-way permutation f {\displaystyle f} , this processing is proved in the random oracle
Snow (Hey Oh) (1,521 words) [view diff] exact match in snippet view article
rapper and internet personality KSI. CD single "Snow (Hey Oh)" – 5:34 "Permutation" (Live) – 3:43 Maxi single 9362 42983-2 "Snow (Hey Oh)" – 5:34 "Funny
Perlin noise (1,804 words) [view diff] exact match in snippet view article find links to article
implementation worked on a 256 node grid and so included the following permutation table: int permutation[] = { 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53
Grøstl (570 words) [view diff] exact match in snippet view article find links to article
a pair of 512- or 1024-bit permutation functions P and Q, and is defined as: f(h, m) = P(h ⊕ m) ⊕ Q(m) ⊕ h The permutation functions P and Q are heavily
Multiply transitive group action (637 words) [view diff] exact match in snippet view article find links to article
replacing 2. Such multiply transitive permutation groups can be defined for any natural number k. Specifically, a permutation group G acting on n points is k-transitive
Munggang (155 words) [view diff] exact match in snippet view article find links to article
slendro. There is a repertory of several repetitive pieces, the best known permutation being high-middle-high-low. It is theorized that pelog was derived from
Neural cryptography (2,224 words) [view diff] exact match in snippet view article find links to article
synchronization could potentially lead to a secure implementation. The permutation parity machine is a binary variant of the tree parity machine. It consists
Schur–Horn theorem (2,908 words) [view diff] exact match in snippet view article find links to article
the sum of the n {\displaystyle n} largest desired eigenvalues. The permutation polytope generated by x ~ = ( x 1 , x 2 , … , x n ) ∈ R n {\displaystyle
Spin–statistics theorem (3,172 words) [view diff] exact match in snippet view article find links to article
if the positions of the particles are exchanged (i.e., they undergo a permutation), this does not identify a new physical state, but rather one matching
LSH (hash function) (3,102 words) [view diff] exact match in snippet view article
{Mix}}_{j}:{\mathcal {W}}^{16}\rightarrow {\mathcal {W}}^{16}} Word-permutation function WordPerm : W 16 → W 16 {\displaystyle {\textrm {WordPerm}}:{\mathcal
Rendezvous problem (588 words) [view diff] exact match in snippet view article find links to article
solution: one player stays put and the other player visits a random permutation of the locations. As well as being problems of theoretical interest,
Samplesort (3,298 words) [view diff] exact match in snippet view article find links to article
bucket, but buckets are not necessarily continuous in memory. Block permutation brings the blocks into the globally correct order. Cleanup moves some
Vertex-transitive graph (646 words) [view diff] exact match in snippet view article find links to article
In the mathematical field of graph theory, an automorphism is a permutation of the vertices such that edges are mapped to edges and non-edges are mapped
Hash function (7,455 words) [view diff] exact match in snippet view article find links to article
more suited to hardware or microcode implementation.: 542–543  Unique permutation hashing has a guaranteed best worst-case insertion time. Standard multiplicative
Outer automorphism group (1,123 words) [view diff] exact match in snippet view article find links to article
An as a subgroup of the symmetric group, Sn, conjugation by any odd permutation is an outer automorphism of An or more precisely "represents the class
Dugald Macpherson (176 words) [view diff] exact match in snippet view article find links to article
Oxford in 1983 for his thesis entitled "Enumeration of Orbits of Infinite Permutation Groups" under the supervision of Peter Cameron. In 1997, he was awarded
Paper Moon (album) (394 words) [view diff] exact match in snippet view article
Paper Moon is Brubeck's third of three Concord recordings featuring this permutation of the Dave Brubeck Quartet; jazz commentator Scott Yanow referred to
Royal Coachman (864 words) [view diff] exact match in snippet view article find links to article
commanding appearance that few fly fisherman can resist having some permutation of the pattern in their fly boxes, even if they never use it. Most of
Wedderburn–Artin theorem (1,085 words) [view diff] exact match in snippet view article find links to article
Di, for some integers ni, both of which are uniquely determined up to permutation of the index i. In particular, any simple left or right Artinian ring
JH (hash function) (399 words) [view diff] exact match in snippet view article
input block into the left half of the state. Apply a 42-round unkeyed permutation (encryption function) to the state. This consists of 42 repetitions of:
Bruhat decomposition (793 words) [view diff] exact match in snippet view article find links to article
However, the determinant of a permutation matrix is the sign of the permutation, so to represent an odd permutation in SLn, we can take one of the nonzero
Commitment scheme (7,701 words) [view diff] exact match in snippet view article find links to article
preimage. Note that since we do not know how to construct a one-way permutation from any one-way function, this section reduces the strength of the cryptographic
Charles Rackoff (301 words) [view diff] exact match in snippet view article find links to article
important result shown there is the construction of a strongly pseudo random permutation generator from a pseudo random function generator). Rackoff was awarded
Algebraic Eraser (1,622 words) [view diff] exact match in snippet view article find links to article
Burau matrix and braid permutation, ( C B ( β ) , σ β ) {\displaystyle (CB(\beta ),\sigma _{\beta })} , applying the permutation and T-values, and then
17 (number) (1,501 words) [view diff] exact match in snippet view article
classification of finite simple groups). In base ten, (17, 71) form the seventh permutation class of permutable primes. The sequence of residues (mod n) of a googol
Running key cipher (1,298 words) [view diff] exact match in snippet view article find links to article
by computer cryptography standards is a relatively easy target. (See permutation generated running keys above for an approach to this problem). Because
MARC-8 (898 words) [view diff] exact match in snippet view article find links to article
specific information of some description, other than a keyword or a permutation string. T 148 94 ISE Item Specification End (DIN 31626) Marks the end
Class automorphism (259 words) [view diff] exact match in snippet view article find links to article
infinitary permutation. This conjugation defines an outer automorphism on the group of finitary permutations. However, for any specific finitary permutation, we
Counterplan (3,927 words) [view diff] exact match in snippet view article find links to article
called permutations, or perms in debate slang. The most common form of permutation and the immediate test of competition is the "do both" permutation, testing
Superflip (689 words) [view diff] exact match in snippet view article find links to article
Rubik's Cube, in which all the edge and corner pieces are in the correct permutation, and the eight corners are correctly oriented, but all twelve edges are
Jessica Fridrich (539 words) [view diff] exact match in snippet view article find links to article
CFOP, that is, (Cross, First 2 Layers, Orientation of the Last Layer, Permutation of the Last Layer). The method describes solving the cube in a layer-by-layer
Index of a subgroup (2,612 words) [view diff] exact match in snippet view article find links to article
be taken to be the kernel of the natural homomorphism from G to the permutation group of the left (or right) cosets of H. Let us explain this in more
Comparison sort (2,640 words) [view diff] exact match in snippet view article find links to article
assume this because this is a worst-case analysis), there are n factorial permutations exactly one of which is the list in sorted order. The sort algorithm
Probabilistic encryption (583 words) [view diff] exact match in snippet view article find links to article
trapdoor permutation. Example of probabilistic encryption using any trapdoor permutation: x - single bit plaintext f - trapdoor permutation (deterministic
Symmetric scale (521 words) [view diff] exact match in snippet view article find links to article
up a whole tone to D, contains exactly the same notes in a different permutation: {D, E, F♯, G♯, A♯, C, D} In the case of inversionally symmetrical scales
V-Cube 7 (1,439 words) [view diff] exact match in snippet view article find links to article
and 150 centers (6 fixed, 144 movable). Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently
Linear group (1,588 words) [view diff] exact match in snippet view article find links to article
representation over K). Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups
Object–verb–subject word order (1,118 words) [view diff] exact match in snippet view article find links to article
typology, object–verb–subject (OVS) or object–verb–agent (OVA) is a rare permutation of word order. OVS denotes the sequence object–verb–subject in unmarked
Sports rating system (3,064 words) [view diff] exact match in snippet view article find links to article
a percentage weight of returning players. Several methods offer some permutation of traditional standings. This search for the "real" win–loss record
Weyl group (3,256 words) [view diff] exact match in snippet view article find links to article
in the figure. As a group, W {\displaystyle W} is isomorphic to the permutation group on three elements, which we may think of as the vertices of the
Null distribution (836 words) [view diff] exact match in snippet view article find links to article
considered using permutation method. Permutation methods are not suitable for correlated sampling units, since the sampling process of permutation implies independence
PSL(2,7) (1,570 words) [view diff] no match in snippet view article
In mathematics, the projective special linear group PSL(2, 7), isomorphic to GL(3, 2), is a finite simple group that has important applications in algebra
Sequential dynamical system (629 words) [view diff] exact match in snippet view article find links to article
F_{w(2)}\circ F_{w(1)}\;.} If the update sequence is a permutation one frequently speaks of a permutation SDS to emphasize this point. The phase space associated
Peter Cameron (mathematician) (489 words) [view diff] exact match in snippet view article
and combinatorics; he has written books about combinatorics, algebra, permutation groups, and logic, and has produced over 350 academic papers. In 1988
Maximal subgroup (385 words) [view diff] exact match in snippet view article find links to article
subgroups are of interest because of their direct connection with primitive permutation representations of G. They are also much studied for the purposes of
Kronecker delta (3,625 words) [view diff] exact match in snippet view article find links to article
distinct integers and are an even permutation of  μ 1 … μ p − 1 if  ν 1 … ν p  are distinct integers and are an odd permutation of  μ 1 … μ p − 0 in all other
Factorial code (558 words) [view diff] exact match in snippet view article find links to article
In addition, they introduce a simple transformation (namely, order permutation) which provides a greedy yet very effective approximation of the optimal
Klein configuration (242 words) [view diff] exact match in snippet view article find links to article
concurrent lines forming an odd permutation, shown below. The sixty planes are 3 coplanar lines forming even permutations, obtained by reversing the last
Symmetric power (227 words) [view diff] exact match in snippet view article find links to article
n := X × ⋯ × X {\displaystyle X^{n}:=X\times \cdots \times X} by the permutation action of the symmetric group S n {\displaystyle {\mathfrak {S}}_{n}}
Quicksort (9,929 words) [view diff] exact match in snippet view article find links to article
x_{n})} is a random permutation, ( x 1 , x 2 , … , x j , x i ) {\displaystyle (x_{1},x_{2},\ldots ,x_{j},x_{i})} is also a random permutation, so the probability
Red Octopus (1,920 words) [view diff] exact match in snippet view article find links to article
spin-off groups. The single "Miracles" was the highest-charting single any permutation of the band had until Starship's "We Built This City" a decade later
Grothendieck's Galois theory (593 words) [view diff] exact match in snippet view article find links to article
quotient finite cyclic group, so that it is specified by giving some permutation of X. In the above example, a connection with classical Galois theory
Format-preserving encryption (2,991 words) [view diff] exact match in snippet view article find links to article
the purposes of the discussion below, the cipher is equivalent to a permutation of N integers {0, ... , N−1} where N is the size of the domain. One motivation
Lock and key (3,921 words) [view diff] exact match in snippet view article find links to article
or coin), by supplying secret information (such as a number or letter permutation or password), by a combination thereof, or it may only be able to be
Quatre Études de rythme (3,373 words) [view diff] exact match in snippet view article find links to article
"permutation in the form of an open fan". The first permutation produces a new ordering which Messiaen called "Interversion I". The same permutation scheme
Faithful representation (352 words) [view diff] exact match in snippet view article find links to article
natural representation of the symmetric group Sn in n dimensions by permutation matrices, which is certainly faithful. Here the order of the group is
Targa Florio Rally (135 words) [view diff] exact match in snippet view article find links to article
The 71 km pattern of Circuito delle Madonie is still used in the same permutation as the original race, and as such the Targa Florio Rally is considered
Koide formula (3,712 words) [view diff] exact match in snippet view article find links to article
263947(6) GeV/c2 for the mass of the top quark. The Koide relation exhibits permutation symmetry among the three charged lepton masses m e {\displaystyle m_{\text{e}}}
List of fugal works by Johann Sebastian Bach (4,521 words) [view diff] exact match in snippet view article find links to article
Herzen” BWV 21.6 – Preludium and permutation Fugue: “Was betrübst du dich, meine Seele” BWV 21.11 – Preludium and permutation Fugue: “Das Lamm, das erwürget
Lattice word (133 words) [view diff] exact match in snippet view article find links to article
In mathematics, a lattice word (or lattice permutation) is a string composed of positive integers, in which every prefix contains at least as many positive
Layer by Layer (502 words) [view diff] exact match in snippet view article find links to article
F' Final layer edge permutation: R U R' U R U2 R' Final layer corner orientation: U R U' L' U R' U' L Final layer corner permutation: R' D' R D The CFOP
McLaughlin sporadic group (717 words) [view diff] exact match in snippet view article find links to article
discovered by Jack McLaughlin (1969) as an index 2 subgroup of a rank 3 permutation group acting on the McLaughlin graph with 275 = 1 + 112 + 162 vertices
Herbert Marvin Ohlman (731 words) [view diff] exact match in snippet view article find links to article
Herbert Marvin Ohlman (1927–2002) is the inventor of permutation indexing, or Permuterm and is one of the pioneers of Information Science and Technology
Orthomorphism (111 words) [view diff] exact match in snippet view article find links to article
θ be a permutation of G. Then θ is an orthomorphism of G if the mapping f defined by f(x) = x−1 θ(x) is also a permutation of G. A permutation φ of G
XOP instruction set (1,448 words) [view diff] exact match in snippet view article find links to article
instructions are integer instructions, but it also contains floating point permutation and floating point fraction extraction instructions. See the index for
E. J. G. Pitman (633 words) [view diff] exact match in snippet view article find links to article
particular, he is remembered primarily as the originator of the Pitman permutation test, Pitman nearness and Pitman efficiency. His work the Pitman measure
Theory of painting (280 words) [view diff] exact match in snippet view article find links to article
painting by means of the rhetorical operations of addition, omission, permutation and transposition. Aesthetics of music Philosophy of music Synesthesia
Macbeth (Sciarrino) (158 words) [view diff] exact match in snippet view article
a production by Achim Freyer. Although the work is based on endless permutation of a few simple recitation-figures, Sciarrino worked on the opera for
Flow-shop scheduling (901 words) [view diff] exact match in snippet view article find links to article
computing designs. A special type of flow-shop scheduling problem is the permutation flow-shop scheduling problem in which the processing order of the jobs
Tannakian formalism (836 words) [view diff] exact match in snippet view article find links to article
that of Grothendieck's Galois theory, which is a theory about finite permutation representations of groups G which are profinite groups. The gist of the
Edgar Lorch (188 words) [view diff] exact match in snippet view article find links to article
general topology, especially metrizable and Baire spaces, group theory of permutation groups and functional analysis, especially spectral theory, convexity
Regular diatonic tuning (2,690 words) [view diff] exact match in snippet view article find links to article
connected together in a chain of seven fifths, all the same size (TTTS or a permutation of that) which makes it a Linear temperament with the tempered fifth
Gazette (468 words) [view diff] exact match in snippet view article find links to article
loanword from the French language, which is, in turn, a 16th-century permutation of the Italian gazzetta, which is the name of a particular Venetian coin
Hard-core predicate (859 words) [view diff] exact match in snippet view article find links to article
pseudorandom generator from any one-way permutation. If b is a hard-core predicate of a one-way permutation f, and s is a random seed, then { b ( f n
Interleaved memory (847 words) [view diff] exact match in snippet view article find links to article
permutation-based interleaved memory method solved the problem with a trivial microarchitecture cost. Sun Microsystems adopted this the permutation interleaving
Schwinger function (2,555 words) [view diff] exact match in snippet view article find links to article
after Julian Schwinger) and they are real-analytic, symmetric under the permutation of arguments (antisymmetric for fermionic fields), Euclidean covariant
SSE5 (626 words) [view diff] exact match in snippet view article find links to article
instructions Integer multiply–accumulate (IMAC, IMADC) instructions Permutation (PPERM, PERMPx) and conditional move (PCMOV) instructions Precision control
Todd–Coxeter algorithm (1,204 words) [view diff] exact match in snippet view article find links to article
of G, the algorithm enumerates the cosets of H on G and describes the permutation representation of G on the space of the cosets (given by the left multiplication
Shabal (1,139 words) [view diff] exact match in snippet view article find links to article
keyed permutation of Shabal updates A and B using nonlinear feedback shift registers that interact with each other. The main loop of the permutation uses
Quasigroup (3,671 words) [view diff] exact match in snippet view article find links to article
squares, an isotopy (α, β, γ) is given by a permutation of rows α, a permutation of columns β, and a permutation on the underlying element set γ. An autotopy
Prior knowledge for pattern recognition (749 words) [view diff] exact match in snippet view article find links to article
class-invariance found in pattern recognition is permutation-invariance, i.e. invariance of the class to a permutation of elements in a structured input. A typical
Plactic monoid (1,043 words) [view diff] exact match in snippet view article find links to article
Schensted (1961) in his study of the longest increasing subsequence of a permutation. It was named the "monoïde plaxique" by Lascoux & Schützenberger (1981)
Degree (588 words) [view diff] exact match in snippet view article find links to article
unsolvability in recursion theory Degree of a central simple algebra Degree of a permutation group, the number of elements that are permuted Degree of a differential
Václav E. Beneš (1,186 words) [view diff] exact match in snippet view article find links to article
contributing to Kalman filter theory as well as the Beneš network, a permutation network of the Clos network type. In the 1980s he held a position at
Lyra2 (2,351 words) [view diff] exact match in snippet view article find links to article
) underlying permutation function (can be seen as the main cryptographic primitive) number of blocks used by the underlying permutation function (bitrate)
Megaminx (2,660 words) [view diff] exact match in snippet view article find links to article
of a more specific set of possible permutations of the latest layer's pieces, performing orientation and permutation of both edges and corners in fewer
Graph dynamical system (1,387 words) [view diff] exact match in snippet view article find links to article
F_{w(2)}\circ F_{w(1)}\;.} If the update sequence is a permutation one frequently speaks of a permutation SDS to emphasize this point. Example: Let Y be the
Labelled enumeration theorem (1,019 words) [view diff] exact match in snippet view article find links to article
generating function (EGF) g(z) which are being distributed into n slots and a permutation group G which permutes the slots, thus creating equivalence classes of
A. W. Faber Model 366 (570 words) [view diff] exact match in snippet view article find links to article
notable for its table of numbers, mapping the numbers 1 to 100 to a permutation of the numbers 0 to 99 in a pattern based on discrete logarithms. The
Rader's FFT algorithm (1,095 words) [view diff] exact match in snippet view article find links to article
the case of DFTs of real data, using a slightly modified re-indexing/permutation to obtain two half-size cyclic convolutions of real data; an alternative
Multiplicative binary search (397 words) [view diff] exact match in snippet view article find links to article
multiplicative binary search is a variation of binary search that uses a specific permutation of keys in an array instead of the sorted order used by regular binary
Ernst Snapper (1,037 words) [view diff] exact match in snippet view article find links to article
extended the classical cohomology of groups to the cohomology of arbitrary permutation representations of finite groups. Snapper then applied these methods
Tits group (675 words) [view diff] exact match in snippet view article find links to article
subgroup of the Rudvalis group, as the point stabilizer of the rank-3 permutation action on 4060 = 1 + 1755 + 2304 points. The Tits group is one of the
Tits group (675 words) [view diff] exact match in snippet view article find links to article
subgroup of the Rudvalis group, as the point stabilizer of the rank-3 permutation action on 4060 = 1 + 1755 + 2304 points. The Tits group is one of the
Philip Bunker (1,386 words) [view diff] exact match in snippet view article find links to article
introduced molecular symmetry groups consisting of feasible nuclear permutations and permutation-inversions. Under the guidance of Longuet-Higgins, Bunker applied
Signature (disambiguation) (579 words) [view diff] exact match in snippet view article
relation symbols in mathematical logic Signature (permutation), a measure for the number of pairs a permutation maps out of order Signature (quadratic form)
Gene orders (323 words) [view diff] exact match in snippet view article find links to article
Gene order is the permutation of genome arrangement. A fair amount of research has been done trying to determine whether gene orders evolve according
Kirkman's schoolgirl problem (4,155 words) [view diff] exact match in snippet view article find links to article
according to a specific permutation of cycle length 13 to create disjoint solutions for subsequent weeks; he chose a permutation with a single 13-cycle
Exchange operator (942 words) [view diff] exact match in snippet view article find links to article
the exchange operator P ^ {\displaystyle {\hat {P}}} , also known as permutation operator, is a quantum mechanical operator that acts on states in Fock
Monk's formula (207 words) [view diff] exact match in snippet view article find links to article
ti,i+1. Then 𝔖sr = x1 + ⋯ + xr, and Monk's formula states that for a permutation w, S s r S w = ∑ i ≤ r < j ℓ ( w t i j ) = ℓ ( w ) + 1 S w t i j , {\displaystyle
Symmetry-breaking constraints (211 words) [view diff] exact match in snippet view article find links to article
routing problem might be identical. For a valid routing plan, every permutation of such identical vehicles yields another valid routing plan with the
Birkhoff polytope (1,007 words) [view diff] exact match in snippet view article find links to article
polytope are the permutation matrices, and therefore that any doubly stochastic matrix may be represented as a convex combination of permutation matrices; this
Carlson symmetric form (3,790 words) [view diff] exact match in snippet view article find links to article
for any permutation of its arguments, and the value of R J ( x , y , z , p ) {\displaystyle R_{J}(x,y,z,p)} is the same for any permutation of its first
Ganita Kaumudi (1,160 words) [view diff] exact match in snippet view article find links to article
rule to determine the number of permutations of n objects and a classical algorithm for finding the next permutation in lexicographic ordering though
Receiver Operating Characteristic Curve Explorer and Tester (1,051 words) [view diff] exact match in snippet view article find links to article
assessment of the quality and robustness of newly discovered biomarkers using permutation testing, hold-out testing and cross-validation. Biomarkers are commonly
Disposition (disambiguation) (128 words) [view diff] exact match in snippet view article
the terms of a will "Disposition" (math), an uncommon way to refer to permutation of n elements over k positions. Disposition of human corpses, such as
Koornwinder polynomials (724 words) [view diff] exact match in snippet view article find links to article
to the partition λ is the unique Laurent polynomial invariant under permutation and inversion of variables, with leading monomial xλ, and orthogonal
Gibbs paradox (5,196 words) [view diff] exact match in snippet view article find links to article
that the definition of entropy must be changed so as to ignore particle permutation, in the thermodynamic limit, the paradox is averted. Gibbs considered
Anti-symmetric operator (1,911 words) [view diff] exact match in snippet view article find links to article
j , k , ℓ , … )  is an even permutation of  ( 1 , 2 , 3 , 4 , … ) − 1 if  ( i , j , k , ℓ , … )  is an odd permutation of  ( 1 , 2 , 3 , 4 , … ) 0 if
Marriage and wedding customs in the Philippines (4,269 words) [view diff] exact match in snippet view article find links to article
marriages and weddings in the Philippines were primarily influenced by the permutation of Christian, both Catholic and Protestant, Hindu, Islam, Chinese, Spanish