{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T13:58:40Z","timestamp":1775483920146,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Many invertible actions $\\tau$ on a set $\\mathcal{S}$ of combinatorial objects,\u00a0along with a natural statistic $f$ on $\\mathcal{S}$, exhibit the following\u00a0property which we dub homomesy:\u00a0the average of $f$ over each $\\tau$-orbit in $\\mathcal{S}$ is the\u00a0same as the average of $f$ over the whole set $\\mathcal{S}$. This phenomenon was first noticed by Panyushev in 2007 in the context of\u00a0the rowmotion action on the set of antichains of a root poset;\u00a0Armstrong, Stump, and Thomas proved Panyushev's conjecture in 2011.\u00a0We describe a theoretical framework for results of this kind \u00a0that applies more broadly, giving examples in a variety of contexts.\u00a0These include linear actions on vector spaces, sandpile dynamics, Suter's action on certain subposets of Young's Lattice, Lyness 5-cycles,\u00a0promotion of rectangular semi-standard Young tableaux,\u00a0and the rowmotion and promotion actions on certain posets.\u00a0We give a detailed description of the latter situation\u00a0for products of two chains. \u00a0<\/jats:p>","DOI":"10.37236\/3579","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:36:27Z","timestamp":1578699387000},"source":"Crossref","is-referenced-by-count":18,"title":["Homomesy in Products of Two Chains"],"prefix":"10.37236","volume":"22","author":[{"given":"James","family":"Propp","sequence":"first","affiliation":[]},{"given":"Tom","family":"Roby","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,7,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:14:45Z","timestamp":1579256085000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/3579","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,1]]},"article-number":"P3.4"}}