Signed permutohedra, delta-matroids, and beyond
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909107930267648 |
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| author | Eur, Christopher Fink, Alex Larson, Matt Spink, Hunter |
| author_facet | Eur, Christopher Fink, Alex Larson, Matt Spink, Hunter |
| contents | We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B generalized permutohedra. Applying tropical Hodge theory to a new framework of "tautological classes of delta-matroids," modeled after certain vector bundles associated to realizable delta-matroids, we establish the log-concavity of a Tutte-like invariant for a broad family of delta-matroids that includes all realizable delta-matroids. Our results include new log-concavity statements for all (ordinary) matroids as special cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_06752 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Signed permutohedra, delta-matroids, and beyond Eur, Christopher Fink, Alex Larson, Matt Spink, Hunter Algebraic Geometry Combinatorics We establish a connection between the algebraic geometry of the type B permutohedral toric variety and the combinatorics of delta-matroids. Using this connection, we compute the volume and lattice point counts of type B generalized permutohedra. Applying tropical Hodge theory to a new framework of "tautological classes of delta-matroids," modeled after certain vector bundles associated to realizable delta-matroids, we establish the log-concavity of a Tutte-like invariant for a broad family of delta-matroids that includes all realizable delta-matroids. Our results include new log-concavity statements for all (ordinary) matroids as special cases. |
| title | Signed permutohedra, delta-matroids, and beyond |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2209.06752 |