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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| Published in | Advances in mathematics (New York. 1965) Vol. 402; p. 108355 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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25.06.2022
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 108355 |
| Author | Bernardi, Olivier Postnikov, Alexander Kálmán, Tamás |
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| Keywords | Tutte activities Graphical zonotopes Hypergraphs Polymatroids Ehrhart-type polynomials Generalized permutohedra |
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| Snippet | 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... |
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| SubjectTerms | Ehrhart-type polynomials Generalized permutohedra Graphical zonotopes Hypergraphs Polymatroids Tutte activities |
| Title | Universal Tutte polynomial |
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