{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:27Z","timestamp":1753893867612,"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>For any Coxeter system $(W,S)$ of rank $n$, we study an abstract boolean complex (simplicial poset) of dimension $2n-1$ that contains the Coxeter complex as a relative subcomplex. For finite $W$, this complex is first described in work of Hultman. Faces are indexed by triples $(I,w,J)$, where $I$ and $J$ are subsets of the set $S$ of simple generators, and $w$ is a minimal length representative for the parabolic double coset $W_I w W_J$. There is exactly one maximal face for each element of the group $W$. The complex is shellable and thin, which implies the complex is a sphere for the finite Coxeter groups. In this case, a natural refinement of the $h$-polynomial is given by the \"two-sided\" $W$-Eulerian polynomial, i.e., the generating function for the joint distribution of left and right descents in $W$.<\/jats:p>","DOI":"10.37236\/8015","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:44:33Z","timestamp":1578667473000},"source":"Crossref","is-referenced-by-count":1,"title":["A Two-Sided Analogue of the Coxeter Complex"],"prefix":"10.37236","volume":"25","author":[{"given":"T. Kyle","family":"Petersen","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,12,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p64\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p64\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:19:20Z","timestamp":1579234760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p64"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,21]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/8015","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,12,21]]},"article-number":"P4.64"}}