Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it
sends the order ideal x to the order ideal generated by the minimal elements not in x. It can …

For each poset $ P $, we construct a polytope $ A (P) $ called the $ P $-associahedron.
Similarly to the case of graph associahedra, the faces of $ A (P) $ correspond to certain …

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 cyclic sieving phenomenon of Reiner, Stanton, and White says that we can often count
the fixed points of elements of a cyclic group acting on a combinatorial set by plugging roots …

Birational rowmotion is an action on the space of assignments of rational functions to the
elements of a finite partially-ordered set (poset). It is lifted from the well-studied rowmotion …

We extend the periodicity of birational rowmotion for rectangular posets to the case when the
base field is replaced by a noncommutative ring (under appropriate conditions). This …

In 2012, N. Williams and the second author showed that on order ideals of ranked partially
ordered sets (posets), rowmotion is conjugate to (and thus has the same orbit structure as) a …

We show that for each k and n, the cyclic shift map on the Grassmannian Gr k, n (C) has
exactly nk fixed points. There is a unique totally nonnegative fixed point, given by taking n …

In this paper we study the class of polytopes which can be obtained by taking the convex
hull of some subset of the points $\{e_i-e_j\\vert\i\neq j\}\cup\{\pm e_i\} $ in $\mathbb {R}^ n …

Interval-closed sets of a poset are a natural superset of order ideals. We initiate the study of
interval-closed sets of finite posets from enumerative and dynamical perspectives. Following …