{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,3]],"date-time":"2026-10-03T16:33:41Z","timestamp":1791045221741,"version":"4.1.0"},"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>The notion of Rees product of posets was introduced by Bj\u00f6rner and Welker in [8], where they study connections between poset topology and commutative algebra.  Bj\u00f6rner and Welker conjectured and Jonsson [25] proved that the dimension of the top homology of the Rees product of the truncated Boolean algebra $B_n \\setminus \\{0\\}$ and the $n$-chain $C_n$ is equal to the number of derangements in the symmetric group $\\mathfrak{ S}$$_n$.   Here we prove a refinement of this result, which involves the Eulerian numbers, and a $q$-analog of both the refinement and the original conjecture, which comes from replacing the Boolean algebra by the lattice of subspaces of the $n$-dimensional vector space over the $q$ element field, and involves the (maj,exc)-$q$-Eulerian polynomials studied in previous papers of the authors [32,33].  Equivariant versions of the refinement and the original conjecture are also proved, as are type BC versions (in the sense of Coxeter groups) of the original conjecture and its $q$-analog.<\/jats:p>","DOI":"10.37236\/86","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:21:45Z","timestamp":1578698505000},"source":"Crossref","is-referenced-by-count":7,"title":["Poset Homology of Rees Products, and $q$-Eulerian Polynomials"],"prefix":"10.37236","volume":"16","author":[{"given":"John","family":"Shareshian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michelle L.","family":"Wachs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2009,7,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i2r20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i2r20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:50:00Z","timestamp":1579297800000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i2r20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,31]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2009,2,11]]}},"URL":"https:\/\/doi.org\/10.37236\/86","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7,31]]},"article-number":"R20"}}