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 …

We survey all known examples of finite posets whose order polynomials have product
formulas, and we propose the heuristic that these are the same posets with good dynamical …

The Naruse hook-length formula is a recent general formula for the number of standard
Young tableaux of skew shapes, given as a positive sum over excited diagrams of products …

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 …

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 present a new family of hook-length formulas for the number of standard increasing
tableaux which arise in the study of factorial Grothendieck polynomials. In the case of …

The rowmotion operator acting on the set of order ideals of a finite poset has been the focus
of a significant amount of recent research. One of the major goals has been to exhibit …

We explore the lifting of this “Stanley–Thomas word” to the piecewise-linear, birational, and
noncommutative realms. Although the map is no longer a bijection, so cannot be used to …

Rowmotion is an invertible operator on the order ideals of a poset which has been
extensively studied and is well understood for the rectangle poset. In this paper, we show …