33 citations · 38 across the 7 of their papers we have counts for
16 papers
Permutohedra, associahedra, and beyond
Alexander Postnikov
The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial properties. We give several di…
Chains in the Bruhat order
Alexander Postnikov, Richard P. Stanley
We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over sa…
A Combinatorial Model for Crystals of Kac-Moody Algebras
Cristian Lenart, Alexander Postnikov
We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be view…
Alcoved Polytopes I
Thomas Lam, Alexander Postnikov
The aim of this paper is to study alcoved polytopes, which are polytopes arising from affine Coxeter arrangements. This class of convex polytopes includes many classical polytopes,…
Trees, parking functions, syzygies, and deformations of monomial ideals
Alexander Postnikov, Boris Shapiro
For a graph G, we construct two algebras, whose dimensions are both equal to the number of spanning trees of G. One of these algebras is the quotient of the polynomial ring modulo…
Affine approach to quantum Schubert calculus
Alexander Postnikov
This article presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials fo…