{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:02Z","timestamp":1753893842528,"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>For a partition $\\lambda$ of an integer, we associate $\\lambda$ with a slender poset $P$ the Hasse diagram of which resembles the Ferrers diagram of $\\lambda$. Let $X$ be the set of maximal chains of $P$. We consider Stanley's involution $\\epsilon:X\\rightarrow X$, which is extended from Sch\u00fctzenberger's evacuation on linear extensions of a finite poset. We present an explicit characterization of the fixed points of the map $\\epsilon:X\\rightarrow X$ when $\\lambda$ is a stretched staircase or a rectangular shape. Unexpectedly, the fixed points have a nice structure, i.e., a fixed point can be decomposed in half into two chains such that the first half and the second half are the evacuation of each other. As a consequence, we prove anew Stembridge's $q=-1$ phenomenon for the maximal chains of $P$ under the involution $\\epsilon$ for the restricted shapes.<\/jats:p>","DOI":"10.37236\/6898","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:40:49Z","timestamp":1578670849000},"source":"Crossref","is-referenced-by-count":0,"title":["Fixed Points of the Evacuation of Maximal Chains on Fuss Shapes"],"prefix":"10.37236","volume":"25","author":[{"given":"Sen-Peng","family":"Eu","sequence":"first","affiliation":[]},{"given":"Tung-Shan","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Hsiang-Chun","family":"Hsu","sequence":"additional","affiliation":[]},{"given":"Yu-Pei","family":"Huang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,2,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:38:54Z","timestamp":1579235934000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6898","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,2,16]]},"article-number":"P1.33"}}