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searching for Möbius function 21 found (101 total)

Permutation pattern (4,037 words) [view diff] exact match in snippet view article find links to article

its Möbius function, a goal first explicitly presented by Wilf (2002). The goal in such investigations is to find a formula for the Möbius function of

William Dunham (mathematician) (577 words) [view diff] case mismatch in snippet view article

Prize in 2022 for his article The Early (and Peculiar) History of the Möbius Function. In 2007, Dunham gave a lecture about Euler's product-sum formula and

Bruhat order (649 words) [view diff] exact match in snippet view article find links to article

The strong Bruhat order on the symmetric group (permutations) has Möbius function given by μ ( π , σ ) = ( − 1 ) ℓ ( σ ) − ℓ ( π ) {\displaystyle \mu

Eulerian poset (407 words) [view diff] exact match in snippet view article find links to article

of an Eulerian poset P can be equivalently stated in terms of its Möbius function: μ P ( x , y ) = ( − 1 ) | y | − | x | for all x ≤ y . {\displaystyle

Tamar Ziegler (646 words) [view diff] exact match in snippet view article find links to article

MR 2680398. S2CID 119596965. Green, Ben; Tao, Terence (2012). "The Möbius function is strongly orthogonal to nilsequences". Annals of Mathematics. 175

Young's lattice (1,081 words) [view diff] exact match in snippet view article find links to article

natural bijection with the skew standard tableaux of skew shape p/q. The Möbius function of Young's lattice takes values 0, ±1. It is given by the formula μ

Carl B. Allendoerfer Award (114 words) [view diff] case mismatch in snippet view article find links to article

Problem William Dunham 2019 The Early (and Peculiar) History of the Möbius Function Jordan Bell and Viktor Blåsjö 2019 Pietro Mengoli’s 1650 Proof that

Multicategory (1,204 words) [view diff] exact match in snippet view article find links to article

is nonzero on all unit arrows has a compositional inverse, and the Möbius function of a multiorder is defined as the compositional inverse of the zeta

Green–Tao theorem (1,538 words) [view diff] exact match in snippet view article find links to article

MR 2680398. S2CID 119596965. Green, Ben; Tao, Terence (2012). "The Möbius function is strongly orthogonal to nilsequences". Annals of Mathematics. 175

Henry Crapo (mathematician) (707 words) [view diff] exact match in snippet view article

A Brief Reminiscence". Matroid Union. Crapo, Henry H. (1966). "The Möbius function of a lattice". Journal of Combinatorial Theory. 1 (1): 126–131. doi:10

Dominance order (1,115 words) [view diff] exact match in snippet view article find links to article

shares some properties with distributive lattices: for example, its Möbius function takes on only values 0, 1, −1. Partitions of n can be graphically represented

Matroid (8,774 words) [view diff] exact match in snippet view article find links to article

_{A}\mu (\emptyset ,A)\lambda ^{r(E)-r(A)}} , where μ denotes the Möbius function of the geometric lattice of the matroid and the sum is taken over all

Euler characteristic (3,461 words) [view diff] exact match in snippet view article find links to article

characteristic of such a poset is defined as the integer μ(0,1), where μ is the Möbius function in that poset's incidence algebra. This can be further generalized

Arrangement of hyperplanes (1,806 words) [view diff] exact match in snippet view article find links to article

regions is ranked by the number of separating hyperplanes and its Möbius function has been computed (Edelman 1984). Vadim Schechtman and Alexander Varchenko

Min-max theorem (4,542 words) [view diff] exact match in snippet view article find links to article

Kline, Jeffery (2020). "Bordered Hermitian matrices and sums of the Möbius function". Linear Algebra and Its Applications. 588: 224–237. doi:10.1016/j

Partially ordered set (5,378 words) [view diff] exact match in snippet view article find links to article

descriptions as a fallbackPages displaying short descriptions with no spaces Möbius function on posets – Associative algebra used in combinatorics, a branch of

Finite difference (5,863 words) [view diff] exact match in snippet view article find links to article

represented by convolution with a function on the poset, called the Möbius function μ; for the difference operator, μ is the sequence (1, −1, 0, 0, 0,

GCD matrix (1,377 words) [view diff] exact match in snippet view article find links to article

\star } is the Dirichlet convolution and μ {\displaystyle \mu } is the Möbius function. Further, if f {\displaystyle f} is a multiplicative function and always

List of conjectures (1,461 words) [view diff] exact match in snippet view article find links to article

group theory Gregory Cherlin and Boris Zilber 86 Chowla conjecture Möbius function ⇒Sarnak conjecture Sarvadaman Chowla Collatz conjecture number theory

Exceptional object (3,088 words) [view diff] exact match in snippet view article find links to article

"Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula". Advances in Mathematics. 30 (2): 85–136

Zhegalkin polynomial (5,153 words) [view diff] exact match in snippet view article find links to article

Since − 1 ≡ 1 {\displaystyle -1\equiv 1} in the Zhegalkin algebra, the Möbius function collapses to being the constant 1. The set of divisors of a given number