Lattice Minors and Eulerian Posets
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913595517829120 |
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| author | Gustafson, William |
| author_facet | Gustafson, William |
| contents | We introduce posets of simple vertex labeled minors of graphs and a generalization to the level of polymatroids, collectively termed minor posets. We show that any minor poset is isomorphic to the face poset of a regular CW sphere, and in particular, is Eulerian. We establish cd-index inequalities induced by strong maps, a tight upper bound for cd-indices of minor posets and a tight lower bound for cd-indices of minor posets arising from lattices of maximal length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01200 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lattice Minors and Eulerian Posets Gustafson, William Combinatorics 06B05, 06A07, 05C83 (Primary) 05B35, 57Q05, 52B05 (Secondary) We introduce posets of simple vertex labeled minors of graphs and a generalization to the level of polymatroids, collectively termed minor posets. We show that any minor poset is isomorphic to the face poset of a regular CW sphere, and in particular, is Eulerian. We establish cd-index inequalities induced by strong maps, a tight upper bound for cd-indices of minor posets and a tight lower bound for cd-indices of minor posets arising from lattices of maximal length. |
| title | Lattice Minors and Eulerian Posets |
| topic | Combinatorics 06B05, 06A07, 05C83 (Primary) 05B35, 57Q05, 52B05 (Secondary) |
| url | https://arxiv.org/abs/2205.01200 |