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arXiv · 2310.20639

The two-variable hypergraph Tutte polynomial via embedding activities

Lilla Tóthmérész
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Abstract

We prove that the two-variable Tutte polynomial of hypergraphs can be defined via embedding activities. We also prove that embedding activities of hypergraphs yield a Crapo-style decomposition of $\mathbb{Z}^E$, thus generalizing Bernardi's results from graphs to hypergraphs. We also show that hypergraph embedding activities do not fit into the $Δ$-activity framework of Courtiel. Based on this observation, we construct a graph with an activity notion that yields a Crapo decomposition, but cannot be obtained as a $Δ$-activity.

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Lilla Tóthmérész. 2024-08-15. The two-variable hypergraph Tutte polynomial via embedding activities. https://arxiv.org/abs/2310.20639

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