Results 31 to 40 of about 520,160 (245)
A non-partitionable Cohen-Macaulay simplicial complex [PDF]
, 2016 A long-standing conjecture of Stanley states that every Cohen-Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample.
Duval, Art M. +3 more
core +3 more sources
An involution on RC-graphs and a conjecture on dual Schubert polynomials by Postnikov and Stanley
Algebraic Combinatorics, 2020 In this paper, we provide explicit formula for the dual Schubert polynomials of a special class of permutations using certain involution principals on RC-graphs, resolving a conjecture by Postnikov and Stanley.
Yibo Gao
semanticscholar +1 more source
The Füredi-Hajnal Conjecture Implies the Stanley-Wilf Conjecture
Journal of Combinatorial Theory, Series A, 2000 We show that the Stanley-Wilf enumerative conjecture on permutations follows easily from the Furedi-Hajnal extremal conjecture on 0–1 matrices. We apply the method, discovered by Alon and Friedgut, that derives an (almost) exponential bound on the number of some objects from a (almost) linear bound on their sizes. They proved by it a weaker form of the
Jang, Y. +2 more
openaire +3 more sources
On the Stanley Depth of Powers of Monomial Ideals
Mathematics, 2019 In 1982, Stanley predicted a combinatorial upper bound for the depth of any finitely generated multigraded module over a polynomial ring. The predicted invariant is now called the Stanley depth. Duval et al.
S. A. Seyed Fakhari
doaj +1 more source
Lexicographic shellability, matroids and pure order ideals [PDF]
, 2014 In 1977 Stanley conjectured that the $h$-vector of a matroid independence complex is a pure $O$-sequence. In this paper we use lexicographic shellability for matroids to motivate a combinatorial strengthening of Stanley's conjecture. This suggests that a
Klee, Steven, Samper, Jose Alejandro
core +1 more source
Stanley depth of squarefree Veronese ideals
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 We compute the Stanley depth for the quotient ring of a square free Veronese ideal and we give some bounds for the Stanley depth of a square free Veronese ideal. In particular, it follows that both satisfy the Stanley's conjecture.
Cimpoeas Mircea
doaj +1 more source
Stanley depth of quotient of monomial complete intersection ideals [PDF]
, 2013 We compute the Stanley depth for a particular, but important case, of the quotient of complete intersection monomial ideals. Also, in the general case, we give sharp bounds for the Stanley depth of a quotient of complete intersection monomial ideals.
Cimpoeas, Mircea
core +1 more source
Stanley's conjectures on the Stern poset
Discrete Mathematics, 2023 The Stern poset $\mathcal{S}$ is a graded infinite poset naturally associated to Stern's triangle, which was defined by Stanley analogously to Pascal's triangle. Let $P_n$ denote the interval of $\mathcal{S}$ from the unique element of row $0$ of Stern's triangle to the $n$-th element of row $r$ for sufficiently large $r$.
openaire +3 more sources
Armstrong's Conjecture for $(k, mk + 1)$-Core Partitions [PDF]
, 2015 A conjecture of Armstrong states that if $\gcd (a, b) = 1$, then the average size of an $(a, b)$-core partition is $(a - 1)(b - 1)(a + b + 1) / 24$. Recently, Stanley and Zanello used a recursive argument to verify this conjecture when $a = b - 1$.
Aggarwal, Amol
core +1 more source
Depth and Stanley depth of the edge ideals of the powers of paths and cycles
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 Let k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a path on n vertices.
Iqbal Zahid, Ishaq Muhammad
doaj +1 more source