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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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 402; p. 108355
Main Authors Bernardi, Olivier, Kálmán, Tamás, Postnikov, Alexander
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.06.2022
Subjects
Ehrhart-type polynomials
Generalized permutohedra
Graphical zonotopes
Hypergraphs
Polymatroids
Tutte activities
Tutte activities
Graphical zonotopes
Hypergraphs
Polymatroids
Ehrhart-type polynomials
Generalized permutohedra
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2022.108355