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# A generalization of the swartz equality

## Pournaki, M. R

- Type of Document: Article
- DOI: 10.1017/S0017089513000311
- Abstract:
- For a given (d-1)-dimensional simplicial complex Γ, we denote its h-vector by h(Γ)=(h 0(Γ),h 1(Γ),...,hd (Γ)) and set h -1(Γ)=0. The known Swartz equality implies that if Δ is a (d-1)-dimensional Buchsbaum simplicial complex over a field, then for every 0 ≤ i ≤ d, the inequality ihi (Δ)+(d-i+1)h i-1(Δ) ≥ 0 holds true. In this paper, by using these inequalities, we give a simple proof for a result of Terai (N. Terai, On h-vectors of Buchsbaum Stanley-Reisner rings, Hokkaido Math. J. 25(1) (1996), 137-148) on the h-vectors of Buchsbaum simplicial complexes. We then generalize the Swartz equality (E. Swartz, Lower bounds for h-vectors of k-CM, independence, and broken circuit complexes, SIAM J. Discrete Math. 18(3) (2004/05), 647-661), which in turn leads to a generalization of the above-mentioned inequalities for Cohen-Macaulay simplicial complexes in co-dimension t
- Keywords:
- Source: Glasgow Mathematical Journal ; Vol. 56, issue. 2 , May , 2014 , pp. 381-386 ; ISSN: 00170895
- URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9219156&fileId=S0017089513000311