{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T13:58:55Z","timestamp":1775483935080,"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>Birational rowmotion \u2014\u00a0a birational map associated to any finite poset $P$ \u2014 has been introduced by Einstein and Propp as a far-reaching generalization of the (well-studied) classical rowmotion map on the set of order ideals of $P$. Continuing our exploration of this birational rowmotion, we prove that it has order $p+q$ on the $\\left(\u00a0 p, q\\right)\u00a0 $-rectangle poset (i.e., on the product of a $p$-element chain with a $q$-element chain); we also compute its orders on some triangle-shaped posets. In all cases mentioned, it turns out to have finite (and explicitly computable) order, a property it does not exhibit for general finite posets (unlike classical rowmotion, which is a permutation of a finite set). Our proof in the case of the rectangle poset uses an idea introduced by Volkov (arXiv:hep-th\/0606094) to prove the $AA$ case of the Zamolodchikov periodicity conjecture; in fact, the finite order of birational rowmotion on many posets can be considered an analogue to Zamolodchikov periodicity. We comment on suspected, but so far enigmatic, connections to the theory of root posets.<\/jats:p>","DOI":"10.37236\/4335","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:25:53Z","timestamp":1578669953000},"source":"Crossref","is-referenced-by-count":14,"title":["Iterative Properties of Birational Rowmotion II: Rectangles and Triangles"],"prefix":"10.37236","volume":"22","author":[{"given":"Darij","family":"Grinberg","sequence":"first","affiliation":[]},{"given":"Tom","family":"Roby","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,9,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:12:48Z","timestamp":1579255968000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,20]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/4335","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,20]]},"article-number":"P3.40"}}