{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T13:25:26Z","timestamp":1775481926179,"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>It is a well-known theorem of Deodhar that the Bruhat ordering of a  Coxeter group is the conjunction of its projections onto quotients by maximal parabolic subgroups. Similarly, the Bruhat order is also the conjunction of a larger number of simpler quotients obtained by  projecting onto two-sided (i.e., \"double\") quotients by pairs of maximal parabolic subgroups. Each one-sided quotient may be represented  as an orbit in the reflection representation, and each double quotient  corresponds to the portion of an orbit on the positive side of certain  hyperplanes. In some cases, these orbit representations are \"tight\"  in the sense that the root system induces an ordering on the orbit that yields effective coordinates for the Bruhat order, and hence also provides upper bounds for the order dimension. In this paper, we (1) provide a general characterization of tightness for one-sided quotients, (2) classify all tight one-sided quotients of finite Coxeter groups, and (3) classify all tight double quotients of affine Weyl groups.<\/jats:p>","DOI":"10.37236\/1871","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:19:21Z","timestamp":1578719961000},"source":"Crossref","is-referenced-by-count":7,"title":["Tight Quotients and Double Quotients in the Bruhat Order"],"prefix":"10.37236","volume":"11","author":[{"given":"John R.","family":"Stembridge","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2005,2,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i2r14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:51:15Z","timestamp":1579323075000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i2r14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,2,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2004,6,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1871","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,2,14]]},"article-number":"R14"}}