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arXiv · 1503.06430

Balanced generalized lower bound inequality for simplicial polytopes

Martina Juhnke-Kubitzke·Satoshi Murai
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Abstract

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.

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Martina Juhnke-Kubitzke, Satoshi Murai. 2015-03-22. Balanced generalized lower bound inequality for simplicial polytopes. https://arxiv.org/abs/1503.06430

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