Journal article

Group actions on semimatroids

  • Delucchi, Emanuele Departement de Mathématiques, Université de Fribourg, Switzerland
  • Riedel, Sonja Departement de Mathématiques, Université de Fribourg, Switzerland - Institute for Algebra, Geometry, Topology and Their Applications, Fachbereich Mathematik und Informatik, Universität Bremen, Germany
Published in:
  • Advances in Applied Mathematics. - 2018, vol. 95, p. 199–270
English We initiate the study of group actions on (possibly infinite) semimatroids and geometric semilattices. To every such action is naturally associated an orbit-counting function, a two-variable “Tutte” polynomial and a poset which, in the representable case, coincides with the poset of connected components of intersections of the associated toric arrangement.In this structural framework we recover and strongly generalize many enumerative results about arithmetic matroids, arithmetic Tutte polynomials and toric arrangements by finding new combinatorial interpretations beyond the representable case. In particular, we thus find a class of natural examples of nonrepresentable arithmetic matroids. Moreover, we discuss actions that give rise to matroids over Z with natural combinatorial interpretations. As a stepping stone toward our results we also prove an extension of the cryptomorphism between semimatroids and geometric semilattices to the infinite case.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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