Work

The Two-Variable Hypergraph Tutte Polynomial via Embedding Activities and Computation-Tree Activities

Year: 2026

Type: article

Abstract: We generalize Bernardi's embedding activity definition for the Tutte polynomial from graphs to hypergraphs, and Gordon-Traldi-McMahon's computation-tree activities from matroids to polymatroids. Furthermore, we introduce a new variant of computation-tree activities, and show that they also yield a definition for the polymatroid Tutte polynomial. In all three cases, the key is to show that the given activity notion yields a Crapo decomposition. We also examine the relationship of these activity notions, and pose some questions about them.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/13306

Author: Lilla Tóthmérész

Institution: Eötvös Loránd University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Magyar Tudományos Akadémia, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Innovációs és Technológiai Minisztérium, National Research, Development and Innovation Office