Universal Tutte polynomial
The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polymatroids, as a two-variable polynomial. Our definition is related to previous works of Cameron and Fink and of Kálmán and...
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Veröffentlicht in: | Advances in mathematics (New York. 1965) 2022-06, Vol.402, p.108355, Article 108355 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polymatroids, as a two-variable polynomial. Our definition is related to previous works of Cameron and Fink and of Kálmán and Postnikov. We then define the universal Tutte polynomial Tn, which is a polynomial of degree n in 2+(2n−1) variables that specializes to the Tutte polynomials of all polymatroids (hence all matroids) on a ground set with n elements. The universal polynomial Tn admits three kinds of symmetries: translation invariance, Sn-invariance, and duality. |
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ISSN: | 0001-8708 1090-2082 |
DOI: | 10.1016/j.aim.2022.108355 |