Results 1 to 10 of about 520,160 (245)
Counterexamples to the Neggers-Stanley conjecture [PDF]
Electronic Research Announcements of the American Mathematical Society, 2004 The Neggers-Stanley conjecture (also known as the Poset conjecture) asserts that the polynomial counting the linear extensions of a partially ordered set on $\{1,2,...,p\}$ by their number of descents has real zeros only.
Brändén, Petter
core +5 more sources
On operators on polynomials preserving real-rootedness and the Neggers-Stanley Conjecture [PDF]
Journal of Algebraic Combinatorics, 2003 We refine a technique used in a paper by Schur on real-rooted polynomials. This amounts to an extension of a theorem of Wagner on Hadamard products of Toeplitz matrices. We also apply our results to polynomials for which the Neggers-Stanley Conjecture is
Brändén, Petter
core +6 more sources
The down operator and expansions of near rectangular k-Schur functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We prove that the Lam-Shimozono ``down operator'' on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the
Chris Berg, Franco Saliola, Luis Serrano
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Upper Triangular Linear Relations on Mmultiplicities and the Stanley-Stembridge Conjecture
The Electronic Journal of Combinatorics, 2022 In 2015, Brosnan and Chow, and independently Guay-Paquet, proved the Shareshian-Wachs conjecture, which links the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group action on the ...
M. Harada, Martha Precup
semanticscholar +4 more sources
A conjecture of Mallows and Sloane with the universal denominator of Hilbert series
Open MathematicsA conjecture of Mallows and Sloane conveys the dominance of Hilbert series for finding basic invariants of finite linear groups if the Hilbert series of the invariant ring is of a certain explicit canonical form.
Zhang Yang, Nan Jizhu, Ma Yongsheng
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ON THE STANLEY DEPTH OF EDGE IDEALS OF LINE AND CYCLIC GRAPHS
Romanian Journal of Mathematics and Computer Science, 2015 We prove that the edge ideals of line and cyclic graphs and their quotient rings satisfy the Stanley conjecture. We compute the Stanley depth for the quotient ring of the edge ideal associated to a cycle graph of length n, given a precise formula for n ≡
MIRCEA CIMPOEAS
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A non-partitionable Cohen–Macaulay simplicial complex [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex is partition- able. We disprove the conjecture by constructing an explicit counterexample.
Art M. Duval +3 more
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Relaxations of the matroid axioms I: Independence, Exchange and Circuits [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial ...
Jose ́ Alejandro Samper
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Birational geometry of generalized Hessenberg varieties and the generalized Shareshian-Wachs conjecture [PDF]
Journal of combinatorial theory. Series A, 2022 We introduce generalized Hessenberg varieties and establish basic facts. We show that the Tymoczko action of the symmetric group $S_n$ on the cohomology of Hessenberg varieties extends to generalized Hessenberg varieties and that natural morphisms among ...
Y. Kiem, Donggun Lee
semanticscholar +1 more source
The Chip Firing Game and Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we construct from a cographic matroid M, a pure multicomplex whose degree sequence is the h―vector of the the matroid complex of M. This result provesa conjecture of Richard Stanley [Sta96] in the particular case of cographic matroids.
Criel Merino
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