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Topological Bijections for Oriented Matroids

Abstract: In previous work by the ?rst and third author with Matthew Baker, a family of bijections between bases of a regular matroid and the Jacobian group of the matroid wasgiven. Thecoreoftheworkisageometricconstructionusingzonotopaltilingsthat produces bijections between the bases of a realizable oriented matroid and the set of (?,??)-compatibleorientationswithrespecttosomeacycliccircuit(respectively, cocircuit) signature ? (respectively, ??). In this work, we extend this construction to general oriented matroids and circuit (respectively, cocircuit) signatures coming from generic single-element liftings (respectively, extensions). As a corollary, when both signatures are induced by the same lexicographic data, we give a new (bijective) proof of the interpretation of TM(1,1) using orientation activity due to Gioan and Las Vergnas. Here TM(x,y) is the Tutte polynomial of the matroid.

 Congreso: Conference on Formal Power Series and Algebraic Combinatorics : FPSAC (31st : 2019 : Ljubljana)

Editorial: Institut de recherche mathe?matique avance?e

 Año de publicación: 2019

Nº de páginas: 12

Tipo de publicación: Comunicación a Congreso

ISSN: 1286-4889

 Proyecto español: MTM2017-83750-P

Url de la publicación: https://www.mat.univie.ac.at/~slc/