{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T10:50:07Z","timestamp":1773399007145,"version":"3.50.1"},"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 give a method for computing the $q$-Eulerian distribution  $$ W(t,q)=\\sum_{w \\in W} t^{{\\rm des}(w)} q^{l(w)} $$ as a rational function in $t$ and $q$, where $(W,S)$ is an arbitrary Coxeter system, $l(w)$ is the length function in $W$, and ${\\rm des}(w)$ is the number of simple reflections $s \\in S$ for which $l(ws) &lt; l(w)$.  Using this we compute generating  functions encompassing the $q$-Eulerian distributions of the classical infinite families of finite and affine Weyl groups.<\/jats:p>","DOI":"10.37236\/1219","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:25:27Z","timestamp":1578705927000},"source":"Crossref","is-referenced-by-count":23,"title":["The distribution of descents and length in a Coxeter group"],"prefix":"10.37236","volume":"2","author":[{"given":"Victor","family":"Reiner","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,11,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r25\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:18:34Z","timestamp":1579328314000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,11,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1219","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,11,25]]},"article-number":"R25"}}