James Propp ; Tom Roby - Homomesy in products of two chains

dmtcs:2356 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2356
Homomesy in products of two chainsArticle

Authors: James Propp 1; Tom Roby 2

Many cyclic actions $τ$ on a finite set $\mathcal{S}$ ; of combinatorial objects, along with a natural statistic $f$ on $\mathcal{S}$, exhibit ``homomesy'': the average of $f$ over each $τ$-orbit in $\mathcal{S} $ is the same as the average of $f$ over the whole set $\mathcal{S} $. This phenomenon was first noticed by Panyushev in 2007 in the context of antichains in root posets; Armstrong, Stump, and Thomas proved Panyushev's conjecture in 2011. We describe a theoretical framework for results of this kind and discuss old and new results for the actions of promotion and rowmotion on the poset that is the product of two chains.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: antichains,combinatorial ergodicity,homomesy,orbit,order ideals,poset,product of chains,promotion,rowmotion,sandpile,toggle group.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Deterministic analogues of random processes; Funder: National Science Foundation; Code: 1001905

22 Documents citing this article

Consultation statistics

This page has been seen 282 times.
This article's PDF has been downloaded 194 times.