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Shellability and the strong gcd-condition
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 16, no 2Article in journal (Refereed) Published
Abstract [en]

Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.

Place, publisher, year, edition, pages
2009. Vol. 16, no 2
National Category
Discrete Mathematics Geometry
Research subject
URN: urn:nbn:se:su:diva-111891OAI: diva2:777024
Available from: 2015-01-08 Created: 2015-01-08 Last updated: 2015-09-17Bibliographically approved

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