Balanced generalized lower bound inequality for simplicial polytopes

Autor(en): Juhnke-Kubitzke, Martina 
Murai, Satoshi
Stichwörter: COMPLEXES; CONJECTURE; Mathematics; Mathematics, Applied
Erscheinungsdatum: 2018
Herausgeber: SPRINGER BASEL AG
Journal: SELECTA MATHEMATICA-NEW SERIES
Volumen: 24
Ausgabe: 2
Startseite: 1677
Seitenende: 1689
Zusammenfassung: 
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.
ISSN: 10221824
DOI: 10.1007/s00029-017-0363-1

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