Skip to Main content Skip to Navigation
New interface
Conference papers

Valuative invariants for polymatroids

Abstract : Many important invariants for matroids and polymatroids, such as the Tutte polynomial, the Billera-Jia-Reiner quasi-symmetric function, and the invariant $\mathcal{G}$ introduced by the first author, are valuative. In this paper we construct the $\mathbb{Z}$-modules of all $\mathbb{Z}$-valued valuative functions for labelled matroids and polymatroids on a fixed ground set, and their unlabelled counterparts, the $\mathbb{Z}$-modules of valuative invariants. We give explicit bases for these modules and for their dual modules generated by indicator functions of polytopes, and explicit formulas for their ranks. Our results confirm a conjecture of the first author that $\mathcal{G}$ is universal for valuative invariants.
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 24, 2015 - 3:47:05 PM
Last modification on : Wednesday, August 7, 2019 - 2:34:15 PM
Long-term archiving on: : Wednesday, November 25, 2015 - 2:47:45 PM


Publisher files allowed on an open archive




Harm Derksen, Alex Fink. Valuative invariants for polymatroids. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.271-282, ⟨10.46298/dmtcs.2849⟩. ⟨hal-01186277⟩



Record views


Files downloads