Work

Tensor Products of Multimatroids and a Brylawski-Type Formula for the Transition Polynomial

Year: 2026

Type: article

Abstract: Brylawski’s tensor product formula expresses the Tutte polynomial of the tensor product of two graphs or matroids in terms of Tutte polynomials arising from the tensor factors. Analogous tensor product formulas are known for the Bollobás–Riordan and transition polynomials of graphs embedded in surfaces. We show that these formulas are instances of a more general result for multimatroids by giving a tensor product formula for the multimatroid transition polynomial and showing that Brylawski’s formula and its topological analogues arise from it. Along the way we provide formulas for the transition polynomial of the two-sum and star product of multimatroids.

Source: Annals of Combinatorics

DOI: 10.1007/s00026-026-00865-3

Authors: Iain Moffatt, Steven Noble, Maya Thompson

Institutions: University of London, Royal Holloway University of London, University of Leeds

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Engineering and Physical Sciences Research Council