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Shellability of the higher pinched Veronese posets
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 40, no 3, 711-742 p.Article in journal (Refereed) Published
Abstract [en]

The pinched Veronese poset is the poset with ground set consisting of all nonnegative integer vectors of length such that the sum of their coordinates is divisible by with exception of the vector . For two vectors and in , we have if and only if belongs to the ground set of . We show that every interval in is shellable for . In order to obtain the result, we develop a new method for showing that a poset is shellable. This method differs from classical lexicographic shellability. Shellability of intervals in has consequences in commutative algebra. As a corollary, we obtain a combinatorial proof of the fact that the pinched Veronese ring is Koszul for . (This also follows from a result by Conca, Herzog, Trung, and Valla.).

Place, publisher, year, edition, pages
2014. Vol. 40, no 3, 711-742 p.
Keyword [en]
Shellable, Pinched Veronese poset, Cohen-Macaulay, Koszul
National Category
URN: urn:nbn:se:kth:diva-155777DOI: 10.1007/s10801-014-0504-yISI: 000343213900004ScopusID: 2-s2.0-84910154522OAI: diva2:763112

QC 20141113

Available from: 2014-11-13 Created: 2014-11-13 Last updated: 2014-11-13Bibliographically approved

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Tancer, Martin
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