{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:06Z","timestamp":1753893846211,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Building everything from scratch, we give another proof of Propp and Roby's theorem saying that the average antichain size in any reverse operator orbit of the poset $[m]\\times [n]$ is $\\frac{mn}{m+n}$. It is conceivable that our method should work for other situations. As a demonstration, we show that the average size of antichains in any reverse operator orbit of $[m]\\times K_{n-1}$ \u00a0equals $\\frac{2mn}{m+2n-1}$. Here $K_{n-1}$ is the minuscule poset $[n-1]\\oplus ([1] \\sqcup [1]) \\oplus [n-1]$. Note that $[m]\\times [n]$ and $[m]\\times K_{n-1}$ can be \u00a0interpreted as sub-families of certain root posets. We guess these root posets should provide a unified setting to exhibit the homomesy phenomenon defined by Propp and Roby.<\/jats:p>","DOI":"10.37236\/7055","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:43:27Z","timestamp":1578671007000},"source":"Crossref","is-referenced-by-count":0,"title":["Orbits of Antichains in Certain Root Posets"],"prefix":"10.37236","volume":"24","author":[{"given":"Chao-Ping","family":"Dong","sequence":"first","affiliation":[]},{"given":"Suijie","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,10,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i4p25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:42:39Z","timestamp":1579236159000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i4p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,20]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7055","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,10,20]]},"article-number":"P4.25"}}