Signed permutohedra, delta-matroids, and beyond
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Publisher
Publisher URL
DOI
10.1112/plms.12592
Journal
Proceedings of the London Mathematical Society
ISSN
0024-6115
Metadata
Show full item recordAbstract
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.
Authors
Eur, C; Fink, A; Larson, M; Spink, HCollections
- Mathematics [1473]