Balanced generalized lower bound inequality for simplicial polytopes

Martina Juhnke-Kubitzke, Satoshi Murai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1677-1689
Number of pages13
JournalSelecta Mathematica, New Series
Issue number2
Publication statusPublished - 2018 Apr 1
Externally publishedYes


  • 05C15
  • 13F55
  • 52B05

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)


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