Peer-reviewedCC BY 4.0The Electronic Journal of Combinatorics
The Two-Variable Hypergraph Tutte Polynomial via Embedding Activities and Computation-Tree Activities
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.
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BibTeX
@article{tothmeresz2026twovariable,
title = {{The Two-Variable Hypergraph Tutte Polynomial via Embedding Activities and Computation-Tree Activities}},
author = {Lilla Tóthmérész},
journal = {The Electronic Journal of Combinatorics},
year = {2026},
month = oct,
doi = {10.37236/13306},
url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p7},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - The Two-Variable Hypergraph Tutte Polynomial via Embedding Activities and Computation-Tree Activities
AU - Lilla Tóthmérész
PY - 2026
DA - 2026/10/09
JO - The Electronic Journal of Combinatorics
DO - 10.37236/13306
UR - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p7
AB - 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.
SN - 1077-8926
ER -