This book gives an introduction to the very active field of combinatorics of affine Schubert
calculus, explains the current state of the art, and states the current open problems. Affine …

The irreducible representations of symmetric groups can be realized as certain graded
pieces of invariant rings, equivalently as global sections of line bundles on partial flag …

We introduce a new concept of resonance on discrete dynamical systems. This concept
formalizes the observation that, in various combinatorially-natural cyclic group actions, orbit …

Abstract Based on Thomas and Yong's K-theoretic jeu de taquin algorithm, we prove a
uniform Littlewood–Richardson rule for the K-theoretic Schubert structure constants of all …

An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It
is well known that the Catalan numbers enumerate both rectangular standard Young …

Abstract We relate Reiner, Tenner, and Yong's coincidental down-degree expectations
(CDE) property of posets to the minuscule doppelgänger pairs studied by Hamaker, Patrias …

The symmetric Grothendieck polynomials representing Schubert classes in the K theory of
Grassmannians are generating functions for semistandard set-valued tableaux. We …

In certain finite posets, the expected down-degree of their elements is the same whether
computed with respect to either the uniform distribution or the distribution weighting an …

We explain how genomic tableaux [Pechenik–Yong'15] are a semistandard complement to
increasing tableaux [Thomas–Yong'09]. From this perspective, one inherits genomic …

We say that two permutations and have separated descents at position if has no descents
before position and has no descents after position. We give a counting formula, in terms of …