On the flag f-vector of a graded lattice with nontrivial homology
arXiv:1012.1451
Abstract
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.
Conjectures 1.4 and 1.5 were disproved by Sam Kolins and have been removed. Conjecture 1.3 remains open