Related papers: Stanley character polynomials

With an arbitrary finite graph having a special form of 2-intervals (a diamond-shaped graph) we associate a subgroup of a symmetric group and a representation of this subgroup; state a series of problems on such groups and their…

Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive…

The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…

Here we consider the image of the principal minor map of symmetric matrices over an arbitrary unique factorization domain $R$. By exploiting a connection with symmetric determinantal representations, we characterize the image of the…

We give an explicit description of character sheaves for the symmetric pairs associated to inner involutions of the special linear groups. We make use of the general strategy given in [VX1] and central character consideration. We also…

We observe the twisted Alexander polynomial for metabelian representations of knot groups into SL(2,C) and study relations to the characterizations of metabelian representations in the character varieties. We give a factorization of the…

In recent years we have worked on a project involving poset topology, various analogues of Eulerian polynomials, and a refinement of Richard Stanley's chromatic symmetric function. Here we discuss how Stanley's ideas and results have…

We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…

We show that a family of multivariate polynomials recently introduced by Bessenrodt and Stanley can be expressed as solution of the octahedron recurrence with suitable initial data. This leads to generalizations and explicit expressions as…

We prove that certain classical groups $G\subseteq {\rm GL}(d,\mathbb{R}^d)$ serve to characterize ordinary polynomials in $d$ real variables as elements of finite-dimensional subspaces of $C(\mathbb{R}^d)$ that are invariant by changes of…

We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. Andre on the number of up-down permutations. The…

Let $I$ be a monomial almost complete intersection ideal of a polynomial algebra $S$ over a field. Then Stanley's Conjecture holds for $S/I$ and $I$.

Stanley asked whether a tree is determined up to isomorphism by its chromatic symmetric function. We approach Stanley's problem by studying the relationship between the chromatic symmetric function and other invariants. First, we prove…

Let $p\ge 5$ be a prime and let $P$ be a Sylow $p$-subgroup of a finite symmetric group. To every irreducible character of $P$ we associate a collection of labelled, complete $p$-ary trees. The main results of this article describe Sylow…

Jack characters are a generalization of the characters of the symmetric groups; a generalization that is related to Jack symmetric functions. We investigate the structure coefficients for Jack characters; they are a generalization of the…

We define nice partitions of the multicomplex associated to a Stanley ideal. As the main result we show that if the monomial ideal $I$ is a CM Stanley ideal, then $I^p$ is a Stanley ideal as well, where $I^p$ is the polarization of $I$.

Consider an $n\times k$ matrix of i.i.d. Bernoulli random numbers with $p=1/2$. Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe $GL_{n}\times…

We prove, combinatorially, that the product of a Schubert polynomial by a Stanley symmetric polynomial is a truncated Schubert polynomial. Using Monk's rule, we derive a nonnegative combinatorial formula for the Schubert polynomial…

Macdonald polynomials are an important class of symmetric functions, with connections to many different fields. Etingof and Kirillov showed an intimate connection between these functions and representation theory: they proved that Macdonald…