Face numbers of cubical barycentric subdivisions

Details Face numbers of cubical barycentric subdivisions Face numbers of cubical barycentric subdivisions

2010-05-22

arxiv.org/abs/1005.4156v2

Mathematics

Combinatorics

8 pages, 1 figure

Scientific paper

The cubical barycentric subdivision sd_c(K) of a cubical complex K is introduced as an analogue of the barycentric subdivision of a simplicial complex. Explicit formulas for the short and long cubical h-vector of sd_c(K) are given, in terms of those of K. It is deduced that symmetry and nonnegativity of these h-vectors, as well as real rootedness of the short cubical h-polynomial, are preserved under cubical barycentric subdivision. The asymptotic behavior of the short and long cubical h-vectors of successive cubical barycentric subdivisions of K is also determined.

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