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math.CO2011
An Upper Bound Theorem concerning lattice polytopes
Gabor Hegedüs
R. P. Stanley proved the Upper Bound Conjecture in 1975. We imitate his proof for the Ehrhart rings. We give some upper bounds for the volume of integrally closed lattice polytopes…
math.AC2011
Betti numbers of Stanley--Reisner rings with pure resolutions
Gabor Hegedüs
Let be simplicial complex and let denote the Stanley--Reisner ring corresponding to . Suppose that has a pure free resolution. Then we describe the Betti numbe…
math.AC2011
The --vector of the clique complex of chordal graphs and Betti numbers of edge ideals of uniform hypergraphs
Gabor Hegedüs
We describe the Betti numbers of the edge ideals of uniform hypergraphs such that has linear graded free resolution. We give an algebraic equation system and some…