Almost Simplicial Polytopes: The Lower and Upper Bound Theorems
| Autor: | Guillermo Pineda-Villavicencio, David Yost, Julien Ugon, Eran Nevo |
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| Rok vydání: | 2019 |
| Předmět: |
Facet (geometry)
Mathematics::Combinatorics General Computer Science Generalization General Mathematics 010102 general mathematics Polytope 02 engineering and technology Simplicial polytope 01 natural sciences h-vector Upper and lower bounds Theoretical Computer Science Vertex (geometry) Combinatorics [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Mathematics::Metric Geometry 020201 artificial intelligence & image processing 0101 mathematics Moment curve Upper bound theorem Mathematics |
| Zdroj: | Scopus-Elsevier |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/s0008414x18000123 |
| Popis: | We study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$, and $s$, thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$. We characterize the minimizers and provide examples of maximizers for any $d$. Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest. |
| Databáze: | OpenAIRE |
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