{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:19:55Z","timestamp":1759335595429,"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 define Dumont's statistic on the symmetric group $S_n$ to be the function dmc: $S_n \\rightarrow {\\bf N}$ which maps a permutation $\\sigma$ to the number of distinct nonzero letters in code$( \\sigma )$. Dumont showed that this statistic is Eulerian.  Naturally extending Dumont's statistic to the rearrangement classes of arbitrary words, we create a generalized statistic which is again Eulerian.  As a consequence, we show that for each distributive lattice $J(P)$ which is a product of chains, there is a poset $Q$ such that the $f$-vector of $Q$ is the $h$-vector of $J(P)$. This strengthens for products of chains a result of Stanley concerning the flag $h$-vectors of Cohen-Macaulay complexes.  We conjecture that the result holds for all finite distributive lattices.<\/jats:p>","DOI":"10.37236\/1555","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:09:24Z","timestamp":1578708564000},"source":"Crossref","is-referenced-by-count":2,"title":["Dumont's Statistic on Words"],"prefix":"10.37236","volume":"8","author":[{"given":"Mark","family":"Skandera","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,1,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:20:25Z","timestamp":1579324825000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1555","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,1,15]]},"article-number":"R11"}}