2015/03/22 by Martina Juhnke‐Kubitzke, Martina Juhnke-Kubitzke, Juhnke-Kubitzke, Martina +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Graph Labeling and Dimension Problems #math.AC #math.CO
paper · pdf · doi:10.48550/arxiv.1503.06430
11 pages
arxiv created 2015/03/22 · openalex publication_date 2015/03/22 · arxiv updated 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.