Signed permutohedra, delta‐matroids, and beyond
We establish a connection between the algebraic geometry of the type B$B$ permutohedral toric variety and the combinatorics of delta‐matroids. Using this connection, we compute the volume and lattice point counts of type B$B$ generalized permutohedra. Applying tropical Hodge theory to a new framewor...
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| Published in: | Proceedings of the London Mathematical Society Vol. 128; no. 3 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01-03-2024
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| Online Access: | Get full text |
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| Summary: | We establish a connection between the algebraic geometry of the type B$B$ permutohedral toric variety and the combinatorics of delta‐matroids. Using this connection, we compute the volume and lattice point counts of type B$B$ 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. |
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| ISSN: | 0024-6115 1460-244X |
| DOI: | 10.1112/plms.12592 |