Balanced generalized lower bound inequality for simplicial polytopes
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A remarkable and important property of face numbers of simplicial polytopes is the generalized lower bound inequality, which says that the h-numbers of any simplicial polytope are unimodal. Recently, for balanced simplicial d-polytopes, that is simplicial d-polytopes whose underlying graphs are d-colorable, Klee and Novik proposed a balanced analogue of this inequality, that is stronger than just unimodality. The aim of this article is to prove this conjecture of Klee and Novik. For this, we also show a Lefschetz property for rank-selected subcomplexes of balanced simplicial polytopes and thereby obtain new inequalities for their h-numbers.
Mathematics Subject Classification52B05 13F55 05C15
The first author was partially supported by DFG GK-1916. The second author was partially supported by JSPS KAKENHI 25400043. We would like to thank Steven Klee and Isabella Novik for their helpful comments on the paper.
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