Face Numbers of Certain Cohen-Macaulay Flag Complexes

Details Face Numbers of Certain Cohen-Macaulay Flag Complexes Face Numbers of Certain Cohen-Macaulay Flag Complexes

2010-10-11

arxiv.org/abs/1010.2253v1

Mathematics

Combinatorics

12 pages, 5 figures

Scientific paper

We show that if a $d$-dimensional Cohen-Macaulay complex is, in a certain
sense, sufficiently "close" to being balanced, then there is a $d$-dimensional
balanced Cohen-Macaulay complex having the same $f$-vector. This in turn
provides some partial evidence for a conjecture of Kalai on the $f$-vectors of
Cohen-Macaulay flag complexes.

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