Lower bounds for h-vectors of k-CM, independence and broken circuit complexes

2004/08/24 by Edward Swartz, Swartz, Edward
Mathematics · #05B35 #52B05 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05B35 #msc:52B05

paper · pdf · doi:10.48550/arxiv.math/0408343

16 pages. To appear in SIAM J. Disc. Math

arxiv created 2004/08/24 · arxiv updated 2009/12/01

Abstract

We present a number of lower bounds for the h-vectors of k-CM, broken circuit and independence complexes. These lead to bounds on the coefficients of the characteristic and reliability polynomials of matroids. The main techniques are the use of series and parallel constructions on matroids and the short simplicial h-vector for pure complexes.

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