Elementary moves on lattice polytopes
| Autor: | Julien David, Lionel Pournin, Rado Rakotonarivo |
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| Rok vydání: | 2020 |
| Předmět: |
Mathematics::Combinatorics
010102 general mathematics Metric Geometry (math.MG) Polytope 0102 computer and information sciences 01 natural sciences Graph Theoretical Computer Science Vertex (geometry) Combinatorics Mathematics - Metric Geometry Computational Theory and Mathematics Computer Science::Discrete Mathematics 010201 computation theory & mathematics Euclidean geometry FOS: Mathematics Mathematics - Combinatorics Mathematics::Metric Geometry Discrete Mathematics and Combinatorics Combinatorics (math.CO) 0101 mathematics Mathematics |
| Zdroj: | Journal of Combinatorial Theory, Series A. 172:105200 |
| ISSN: | 0097-3165 |
| DOI: | 10.1016/j.jcta.2019.105200 |
| Popis: | We introduce a graph structure on Euclidean polytopes. The vertices of this graph are the $d$-dimensional polytopes contained in $\mathbb{R}^d$ and its edges connect any two polytopes that can be obtained from one another by either inserting or deleting a vertex, while keeping their vertex sets otherwise unaffected. We prove several results on the connectivity of this graph, and on a number of its subgraphs. We are especially interested in several families of subgraphs induced by lattice polytopes, such as the subgraphs induced by the lattice polytopes with $n$ or $n+1$ vertices, that turn out to exhibit intriguing properties. 35 pages, 9 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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