Results 11 to 20 of about 520,160 (245)
Schubert polynomials, 132-patterns, and Stanley's conjecture [PDF]
Algebraic Combinatorics, 2017 Motivated by a recent conjecture of R. P. Stanley we offer a lower bound for the sum of the coefficients of a Schubert polynomial in terms of $132$-pattern containment.
Anna Weigandt
semanticscholar +4 more sources
Resolving Stanley's conjecture on $k$-fold acyclic complexes [PDF]
Combinatorial Theory, 2018 In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank $1$ boolean intervals whose minimal faces together form a subcomplex. Stanley further conjectured that complexes with
Joseph Doolittle, Bennet Goeckner
semanticscholar +8 more sources
ALMOST COMPLETE INTERSECTIONS AND STANLEY'S CONJECTURE [PDF]
Kodai Mathematical Journal, 2013 Let K be a field and I a monomial ideal of the polynomial ring S = K(x1,...,xn). We show that if either: 1) I is almost complete intersection, 2) I can be generated by less than four monomials; or 3) I is the Stanley-Reisner ideal of a locally complete ...
Somayeh Bandari +2 more
semanticscholar +5 more sources
Isomorphism of weighted trees and Stanley's isomorphism conjecture for caterpillars [PDF]
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, 2019 This paper contributes to a programme initiated by the first author: `How much information about a graph is revealed in its Potts partition function?'. We show that the W-polynomial distinguishes non-isomorphic weighted trees of a good family.
M. Loebl, Jean-Sébastien Sereni
semanticscholar +3 more sources
The Stanley Conjecture on Intersections of Four Monomial Prime Ideals [PDF]
Communications in Algebra, 2010 We show that the Stanley's Conjecture holds for an intersection of four monomial prime ideals of a polynomial algebra S over a field and for an arbitrary intersection of monomial prime ideals (P i ) i∈[s] of S such that each P i is not contained in the ...
D. Popescu
semanticscholar +3 more sources
The cohomology of abelian Hessenberg varieties and the Stanley–Stembridge conjecture [PDF]
Algebraic Combinatorics, 2017 We define a subclass of Hessenberg varieties called abelian Hessenberg varieties, inspired by the theory of abelian ideals in a Lie algebra developed by Kostant and Peterson.
M. Harada, Martha Precup
semanticscholar +6 more sources
STANLEY CONJECTURE IN SMALL EMBEDDING DIMENSION [PDF]
Journal of Algebra, 2007 We show that Stanley's conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals.
Imran Anwar, D. Popescu
semanticscholar +3 more sources
Stanley's conjecture, cover depth and extremal simplicial complexes
Le Matematiche, 2008 A famous conjecture by R. Stanley relates the depth of a module, an algebraic invariant, with the so-called Stanley depth, a geometric one. We describe two related geometric notions, the cover depth and the greedy depth, and we study their relations with
Benjamin Nill, Kathrin Vorwerk
doaj +1 more source
On the Neggers-Stanley Conjecture and the Eulerian Polynomials
Journal of Combinatorial Theory, Series A, 1998 If \(P=(P,
Vesselin Gasharov
semanticscholar +3 more sources
Stanley conjecture on monomial ideals of mixed products [PDF]
Journal of Commutative Algebra, 2015 Let \(I'\subseteq I\) be monomial ideals in a polynomial ring \(S_1=k[x_1,\ldots,x_m]\), and \(J' \subseteq J\) be monomial ideals in a polynomial ring \(S_2=k[y_1,\ldots,y_n]\). The ideal \(I\) generated by \(I'J+IJ'\) in \(S=S_1\otimes_k S_2\) is called by the authors a \textit{generalized mixed product} ideal. Let \(I_q\) denotes the ideal generated
G. Restuccia, Zhongming Tang, R. Utano
semanticscholar +3 more sources