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 …

We survey recent work within the area of algebraic combinatorics that has the flavor of
discrete dynamical systems, with a particular focus on the homomesy phenomenon codified …

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 …

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 …

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 …

Given a permutation $\tau $ defined on a set of combinatorial objects $ S $, together with
some statistic $ f: S\rightarrow\mathbb {R} $, we say that the triple $\langle S,\tau, f\rangle …

Abstract The Lalanne–Kreweras involution is an involution on the set of Dyck paths which
combinatorially exhibits the symmetry of the number of valleys and major index statistics. We …

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 …

A fence is a poset with elements F={x1, x2,..., xn} and covers x1¡ x2¡...¡ xa£ xa+ 1£...£ xb¡ xb+
1¡··· where a, b,... are positive integers. We investigate rowmotion on antichains and ideals of …

We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order
intervals corresponding to certain vexillary permutations have the coincidental down-degree …