Lower bounds for Buchsbaum* complexes

The class of ( d − 1 ) -dimensional Buchsbaum* simplicial complexes is studied. It is shown that the rank-selected subcomplexes of a (completely) balanced Buchsbaum* simplicial complex are also Buchsbaum*. Using this result, lower bounds on the h -numbers of balanced Buchsbaum* simplicial complexes are established. In addition, sharp lower bounds on the h -numbers of flag m -Buchsbaum* simplicial complexes are derived, and the case of equality is treated.