Delucchi, Emanuele Riedel, Sonja 2018-04-01 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. application/pdf https://sonar.ch/global/documents/306361 https://sonar.ch/documents/306361/files/del_gas.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aam.2017.11.001 info:eu-repo/semantics/openAccess License undefined Advances in Applied Mathematics. - 2018, vol. 95, p. 199–270 info:eu-repo/classification/udc/51 Group actions on semimatroids http://purl.org/coar/resource_type/c_6501