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searching for Integer lattice 33 found (97 total)

Complex multiplication (2,071 words) [view diff] exact match in snippet view article find links to article

are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice. It has an aspect belonging to the theory of special

Lattice reduction (922 words) [view diff] exact match in snippet view article find links to article

to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose

Brownian web (816 words) [view diff] exact match in snippet view article find links to article

coalescing random walks, with one walk starting from each point of the integer lattice Z at each time. What is now known as the Brownian web was first conceived

Binary image (1,756 words) [view diff] exact match in snippet view article find links to article

Binary images can be interpreted as subsets of the two-dimensional integer lattice Z2; the field of morphological image processing was largely inspired

Presentation complex (462 words) [view diff] exact match in snippet view article find links to article

G = Z 2 {\displaystyle G=\mathbb {Z} ^{2}} be the two-dimensional integer lattice, with presentation G = ⟨ x , y | x y x − 1 y − 1 ⟩ . {\displaystyle

William Floyd (mathematician) (382 words) [view diff] exact match in snippet view article

Dr. Floyd discusses languages over the integer lattice.

Plane partition (4,999 words) [view diff] exact match in snippet view article find links to article

defined as a finite subset P {\displaystyle {\mathcal {P}}} of positive integer lattice points (i, j, k) in N 3 {\displaystyle \mathbb {N} ^{3}} , such that

Ira Gessel (560 words) [view diff] exact match in snippet view article find links to article

combinatorics known as lattice walks, which usually take place on the integer lattice and are sometimes confined to the upper right quadrant. An excursion

Integer points in convex polyhedra (434 words) [view diff] exact match in snippet view article find links to article

The red dots are the integer lattice points within the blue polygon, the latter representing a two-dimensional linear program

G2 (mathematics) (2,056 words) [view diff] exact match in snippet view article

the Cartan matrix above. These are (2,−3) and (−1, 2), however the integer lattice spanned by those is not the one pictured above (from obvious reason:

Reeve tetrahedra (875 words) [view diff] exact match in snippet view article find links to article

Family of tetrahedra on an integer lattice

Loop-erased random walk (2,458 words) [view diff] exact match in snippet view article find links to article

1214/aop/1079021469 Pemantle, Robin (1991), "Choosing a spanning tree for the integer lattice uniformly", Annals of Probability, 19 (4): 1559–1574, arXiv:math/0404043

Carolyn Mahoney (611 words) [view diff] exact match in snippet view article find links to article

; Mahoney, Carolyn R. (1996), "Unit-distance graphs, graphs on the integer lattice and a Ramsey type result", Aequationes Mathematicae, 51 (1–2): 48–67

Polytope (3,119 words) [view diff] exact match in snippet view article find links to article

(t+1)} -dilate of P {\displaystyle {\mathcal {P}}} differs, in terms of integer lattice points, from a t {\displaystyle t} -dilate of P {\displaystyle {\mathcal

List of circle topics (2,408 words) [view diff] exact match in snippet view article find links to article

centered on a common sixth circle Gauss circle problem – How many integer lattice points there are in a circle Gershgorin circle theorem – Bound on eigenvalues

Polyhedral combinatorics (2,304 words) [view diff] exact match in snippet view article find links to article

convex polytopes does not form a convex subset of the four-dimensional integer lattice, and much remains unknown about the possible values of these vectors

Hyperharmonic number (1,095 words) [view diff] exact match in snippet view article find links to article

{\displaystyle S(x)=x^{2}+O(x\log ^{3}x).} Note that the number of integer lattice points in [ 0 , x ] × [ 0 , x ] {\displaystyle [0,x]\times [0,x]} is

Harry Kesten (1,754 words) [view diff] exact match in snippet view article find links to article

\sigma _{n}} of n-step self-avoiding walks from the origin on the integer lattice satisfies σ n + 2 / σ n → μ 2 {\displaystyle \sigma _{n+2}/\sigma _{n}\to

Analytic number theory (3,834 words) [view diff] exact match in snippet view article find links to article

about the origin in the plane with radius r, the problem asks how many integer lattice points lie on or inside the circle. It is not hard to prove that the

Sum of squares function (1,128 words) [view diff] exact match in snippet view article find links to article

Integers satisfying the sum of two squares theorem are squares of possible distances between integer lattice points; values up to 100 are shown, with

Hadwiger–Nelson problem (1,866 words) [view diff] exact match in snippet view article find links to article

; Mahoney, Carolyn R. (1996), "Unit-distance graphs, graphs on the integer lattice and a Ramsey type result", Aequationes Mathematicae, 51 (1–2): 48–67

Circle (6,352 words) [view diff] exact match in snippet view article find links to article

Distance – Separation between two points Gauss circle problem – How many integer lattice points there are in a circle Inversion in a circle – Study of angle-preserving

Szemerédi–Trotter theorem (2,432 words) [view diff] exact match in snippet view article find links to article

integer N ∈ N {\displaystyle N\in \mathbb {N} } a set of points on the integer lattice P = { ( a , b ) ∈ Z 2 : 1 ≤ a ≤ N ; 1 ≤ b ≤ 2 N 2 } , {\displaystyle

Italo Jose Dejter (5,660 words) [view diff] exact match in snippet view article find links to article

S are restrictions of only one total perfect code S1 in the planar integer lattice graph, with the extra-bonus that the complement of S1 yields an aperiodic

Torus (5,166 words) [view diff] exact match in snippet view article find links to article

any coordinate. That is, the n-torus is Rn modulo the action of the integer lattice Zn (with the action being taken as vector addition). Equivalently,

Lie group–Lie algebra correspondence (4,466 words) [view diff] exact match in snippet view article find links to article

of it is a discrete group (since the dimension is zero) called the integer lattice of G and is denoted by Γ {\displaystyle \Gamma } . By the first isomorphism

Tau function (integrable systems) (6,689 words) [view diff] exact match in snippet view article

\cdots } , which corresponds to the Dirac sea of states along the real integer lattice in which all negative integer locations are occupied and all non-negative

Random walk (7,703 words) [view diff] exact match in snippet view article find links to article

The best-studied example is the random walk on the d-dimensional integer lattice (sometimes called the hypercubic lattice) Z d {\displaystyle \mathbb

3-manifold (5,821 words) [view diff] exact match in snippet view article find links to article

any coordinate. That is, the 3-torus is R3 modulo the action of the integer lattice Z3 (with the action being taken as vector addition). Equivalently,

Chromatic polynomial (4,325 words) [view diff] exact match in snippet view article find links to article

natural numbers to each vertex, a graph coloring is a vector in the integer lattice. Since two vertices i {\displaystyle i} and j {\displaystyle j} being

LP-type problem (4,687 words) [view diff] exact match in snippet view article find links to article

MR 1671836, S2CID 182728. Bell, David E. (1977), "A theorem concerning the integer lattice" (PDF), Studies in Applied Mathematics, 56 (2): 187–188, doi:10.1002/sapm1977562187

Average order of an arithmetic function (4,093 words) [view diff] exact match in snippet view article find links to article

also easy to see that gcd(a, b) = 1 implies that there is no other integer lattice point in the segment joining (0,0) to (a,b). Thus, (a, b) is visible

Brunn–Minkowski theorem (2,993 words) [view diff] exact match in snippet view article find links to article

and combinatorial versions about counting sets of points inside the integer lattice. Isoperimetric inequality Milman's reverse Brunn–Minkowski inequality