Bigraded Betti numbers of certain simple polytopes
نویسندگان
چکیده
منابع مشابه
Empty Simplices of Polytopes and Graded Betti Numbers
Abstract. The conjecture of Kalai, Kleinschmidt, and Lee on the number of empty simplices of a simplicial polytope is established by relating it to the first graded Betti numbers of the polytope. The proof allows us to derive explicit optimal bounds on the number of empty simplices of any given dimension. As a key result, we prove optimal bounds for the graded Betti numbers of any standard grad...
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Let G be a simple graph on n vertices. LetH be either the complete graph Km or the complete bipartite graph Kr,s on a subset of the vertices in G. We show that G contains H as a subgraph if and only if βi,α(H) ≤ βi,α(G) for all i ≥ 0 and α ∈ Z. In fact, it suffices to consider only the first syzygy module. In particular, we prove that β1,α(H) ≤ β1,α(G) for all α ∈ Z if and only if G contains a ...
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ژورنال
عنوان ژورنال: Mathematical Notes
سال: 2013
ISSN: 0001-4346,1573-8876
DOI: 10.1134/s000143461309006x