• Corpus ID: 219179711

# Order polynomial product formulas and poset dynamics

@article{Hopkins2020OrderPP,
title={Order polynomial product formulas and poset dynamics},
author={Sam Hopkins},
journal={arXiv: Combinatorics},
year={2020}
}
• S. Hopkins
• Published 2 June 2020
• Mathematics
• arXiv: Combinatorics
We survey all known examples of finite posets whose order polynomials have product formulas, and we put forward a heuristic which says that these are the same posets which have 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.
10 Citations

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A generalization of K-promotion to the setting of arbitrary increasing labelings of any finite poset with given restrictions on the labels shows it corresponds to a toggle group action the authors call toggle-prom promotion on order ideals of an associated poset when the restrictions on labels are particularly nice.