{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:09:10Z","timestamp":1759939750113,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We study a birational map associated to any finite poset $P$. This map is a\u00a0far-reaching generalization (found by Einstein and Propp) of classical\u00a0rowmotion, which is a certain permutation of the set of order ideals of $P$.\u00a0Classical rowmotion has been studied by various authors (Fon-der-Flaass,\u00a0Cameron, Brouwer, Schrijver, Striker, Williams and many more) under different\u00a0guises (Striker-Williams promotion and Panyushev complementation are two\u00a0examples of maps equivalent to it). In contrast, birational rowmotion is new\u00a0and has yet to reveal several of its mysteries. In this paper, we set up the\u00a0tools for analyzing the properties of iterates of this map, and prove that\u00a0it has finite order for a certain class of posets which we call \"skeletal\".\u00a0Roughly speaking, these are graded posets constructed from one-element posets by\u00a0repeated disjoint union and \"grafting onto an antichain\"; in particular,\u00a0any forest having its leaves all on the same rank is such a poset.\u00a0We also make a parallel analysis of classical rowmotion on this kind of posets,\u00a0and prove that the order in this case equals the order of birational rowmotion.<\/jats:p>","DOI":"10.37236\/4334","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:55:50Z","timestamp":1578693350000},"source":"Crossref","is-referenced-by-count":11,"title":["Iterative Properties of Birational Rowmotion I: Generalities and Skeletal Posets"],"prefix":"10.37236","volume":"23","author":[{"given":"Darij","family":"Grinberg","sequence":"first","affiliation":[]},{"given":"Tom","family":"Roby","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,2,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:36:11Z","timestamp":1579239371000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/4334","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,2,19]]},"article-number":"P1.33"}}