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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geprüft am 17.05.2024