Order polynomial product formulas and poset dynamics

Abstract

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 behavior. Here the dynamics in question are the actions of promotion on the linear extensions of the poset and rowmotion on the P-partitions of the poset.

22 pages, 3 figures; v6: final version to appear AMS Proceedings of Symposia in Pure Mathematics volume associated with the "Open Problems in Algebraic Combinatorics" 2022 conference at the University of Minnesota

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