{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:23:46Z","timestamp":1773815026670,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $a &lt; b$ be coprime positive integers. Armstrong, Rhoades, and Williams (2013) defined a set NC(a,b) of `rational noncrossing partitions', which form a subset of the ordinary noncrossing partitions\u00a0of $\\{1, 2, \\dots, b-1\\}$. \u00a0Confirming a conjecture of Armstrong et. al., we prove that NC(a,b) is closed under rotation and prove\u00a0an instance of the cyclic sieving phenomenon for this rotational action. \u00a0We also define a rational generalization of the $\\mathfrak{S}_a$-noncrossing parking functions of\u00a0Armstrong, Reiner, and Rhoades.<\/jats:p>","DOI":"10.37236\/5681","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:32:07Z","timestamp":1578691927000},"source":"Crossref","is-referenced-by-count":6,"title":["Cyclic Sieving and Rational Catalan Theory"],"prefix":"10.37236","volume":"23","author":[{"given":"Michelle","family":"Bodnar","sequence":"first","affiliation":[]},{"given":"Brendon","family":"Rhoades","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,3,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i2p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:30:44Z","timestamp":1579239044000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i2p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,25]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/5681","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,25]]},"article-number":"P2.4"}}