Balanced vertex decomposable simplicial complexes and their h-vectors

2012/01/31 by Biermann, Jennifer, Van Tuyl, Adam · 1 citation
#05A15 #05E45 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1202.0044

Abstract

Given any finite simplicial complex Δ, we show how to construct a new simplicial complex Δ_χ that is balanced and vertex decomposable. Moreover, we show that the h-vector of the simplicial complex Δ_χ is precisely the f-vector, denoted f(Δ), of the original complex Δ. We deduce this result by relating f(Δ) with the graded Betti numbers of the Alexander dual of Δ_χ. Our construction generalizes the "whiskering" construction of Villarreal, and Cook and Nagel. As a corollary of our work, we add a new equivalent statement to a theorem of Björner, Frankl, and Stanley that classifies the f-vectors of simplicial complexes. We also prove a special case of a conjecture of Cook and Nagel, and Constantinescu and Varbaro on the h-vectors of flag complexes.

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