A recursive definition for the polymatroid Tutte polynomial
Combinatorics
2025-10-14 v1
Abstract
The Tutte polynomial is a significant invariant of graphs and matroids. It is well-known that it has three equivalent definitions: bases expansion, rank generating function, and deletion-contraction formula. The polymatroid Tutte polynomial generalizes the Tutte polynomial from matroids to polymatroids . In \emph{[Adv. Math. 402 (2022) 108355.]} and \emph{[J. Combin. Theory Ser. A 188 (2022) 105584]}, the authors provided bases expansion and rank generating function constructions for , respectively. In \emph{[Int. Math. Res. Not. 19 (2025) rnaf302]}, a recursive formula for was obtained. In this paper, we show that the recursive formula itself can be used to define the polymatroid Tutte polynomial independently.
Cite
@article{arxiv.2510.11046,
title = {A recursive definition for the polymatroid Tutte polynomial},
author = {Xiaxia Guan and Xian'an Jin and Weiling Yang},
journal= {arXiv preprint arXiv:2510.11046},
year = {2025}
}