{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:58Z","timestamp":1753893838145,"version":"3.41.2"},"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>Shellability is a well-known combinatorial criterion on a simplicial complex $\\Delta$ for verifying that the associated Stanley-Reisner ring $k[\\Delta]$ is Cohen-Macaulay. A notion familiar to commutative algebraists, but which has not received as much attention from combinatorialists as the Cohen-Macaulay property, is the notion of a Golod ring. Recently, J\u00f6llenbeck introduced a criterion on simplicial complexes reminiscent of shellability, called the strong gcd-condition, and he together with the author proved that it implies Golodness of the associated Stanley-Reisner ring. The two algebraic notions were earlier tied together by Herzog, Reiner and Welker, who showed that if $k[\\Delta^\\vee]$ is sequentially Cohen-Macaulay, where $\\Delta^\\vee$ is the Alexander dual of $\\Delta$, then $k[\\Delta]$ is Golod. In this paper, we present a combinatorial companion of this result, namely that if $\\Delta^\\vee$ is (non-pure) shellable then $\\Delta$ satisfies the strong gcd-condition. Moreover, we show that all implications just mentioned are strict in general but that they are equivalences if $\\Delta$ is a flag complex.<\/jats:p>","DOI":"10.37236\/67","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:22:27Z","timestamp":1578716547000},"source":"Crossref","is-referenced-by-count":1,"title":["Shellability and the Strong gcd-Condition"],"prefix":"10.37236","volume":"16","author":[{"given":"Alexander","family":"Berglund","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,2,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i2r1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i2r1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:12:51Z","timestamp":1579317171000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i2r1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2,11]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2009,2,11]]}},"URL":"https:\/\/doi.org\/10.37236\/67","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,2,11]]},"article-number":"R1"}}