On the flag f-vector of a graded lattice with nontrivial homology

Details On the flag f-vector of a graded lattice with nontrivial homology On the flag f-vector of a graded lattice with nontrivial homology

2010-12-07

arxiv.org/abs/1012.1451v2

Mathematics

Combinatorics

Conjectures 1.4 and 1.5 were disproved by Sam Kolins and have been removed. Conjecture 1.3 remains open

Scientific paper

It is proved that the Boolean algebra of rank n minimizes the flag f-vector
among all graded lattices of rank n, whose proper part has nontrivial
top-dimensional homology. The analogous statement for the flag h-vector is
conjectured in the Cohen-Macaulay case.

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