Partitons of vertices and facets in trees and stacked simplicial complexes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914640552787968 |
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| author | Fløystad, Gunnar |
| author_facet | Fløystad, Gunnar |
| contents | For stacked simplicial complexes, (special subclasses of such are: trees, triangulations of polygons, stacked polytopes), we give an explicit bijection between partitions of facets (for trees: edges), and partitions of vertices into independent sets. More generally we give bijections between facet partitions whose parts have minimal distance $\geq s$ and vertex partitions whose parts have minimal distance $\geq s+1$. A consequence is results on partitions of natural numbers, where the parts have minimal bounds on spacing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04444 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Partitons of vertices and facets in trees and stacked simplicial complexes Fløystad, Gunnar Combinatorics 05C05 05C69, 05E45 For stacked simplicial complexes, (special subclasses of such are: trees, triangulations of polygons, stacked polytopes), we give an explicit bijection between partitions of facets (for trees: edges), and partitions of vertices into independent sets. More generally we give bijections between facet partitions whose parts have minimal distance $\geq s$ and vertex partitions whose parts have minimal distance $\geq s+1$. A consequence is results on partitions of natural numbers, where the parts have minimal bounds on spacing. |
| title | Partitons of vertices and facets in trees and stacked simplicial complexes |
| topic | Combinatorics 05C05 05C69, 05E45 |
| url | https://arxiv.org/abs/2207.04444 |