$P$strict promotion and $Q$partition rowmotion: the graded case
Abstract
Promotion and rowmotion are intriguing actions in dynamical algebraic combinatorics which have inspired much work in recent years. In this paper, we study $P$strict labelings of a finite, graded poset $P$ of rank $n$ and labels at most $q$, which generalize semistandard Young tableaux with $n$ rows and entries at most $q$, under promotion. These $P$strict labelings are in equivariant bijection with $Q$partitions under rowmotion, where $Q$ equals the product of $P$ and a chain of $qn1$ elements. We study the case where $P$ equals the product of chains in detail, yielding new homomesy and order results in the realm of tableaux and beyond. Furthermore, we apply the bijection to the cases in which $P$ is a minuscule poset and when $P$ is the three element $V$ poset. Finally, we give resonance results for promotion on $P$strict labelings and rowmotion on $Q$partitions.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 DOI:
 10.48550/arXiv.2205.04938
 arXiv:
 arXiv:2205.04938
 Bibcode:
 2022arXiv220504938B
 Keywords:

 Mathematics  Combinatorics;
 05E18
 EPrint:
 23 pages, 4 figures