scholarly journals K-theoretic Tutte polynomials of morphisms of matroids

2021 ◽  
Vol 181 ◽  
pp. 105414
Author(s):  
Rodica Dinu ◽  
Christopher Eur ◽  
Tim Seynnaeve
Keyword(s):  
Tutte Polynomials

scholarly journals The Tutte polynomial of symmetric hyperplane arrangements

2020 ◽  
Vol 29 (03) ◽  
pp. 2050004
Author(s):  
Hery Randriamaro
Keyword(s):  
Hyperplane Arrangement ◽  
Dual Graph ◽  
Tutte Polynomial ◽  
Hyperplane Arrangements ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Tutte Polynomials ◽  
One Year ◽  
The One ◽  
Definition Of

The Tutte polynomial is originally a bivariate polynomial which enumerates the colorings of a graph and of its dual graph. Ardila extended in 2007 the definition of the Tutte polynomial on the real hyperplane arrangements. He particularly computed the Tutte polynomials of the hyperplane arrangements associated to the classical Weyl groups. Those associated to the exceptional Weyl groups were computed by De Concini and Procesi one year later. This paper has two objectives: On the one side, we extend the Tutte polynomial computing to the complex hyperplane arrangements. On the other side, we introduce a wider class of hyperplane arrangements which is that of the symmetric hyperplane arrangements. Computing the Tutte polynomial of a symmetric hyperplane arrangement permits us to deduce the Tutte polynomials of some hyperplane arrangements, particularly of those associated to the imprimitive reflection groups.

scholarly journals Chain polynomials and Tutte polynomials

2002 ◽  
Vol 248 (1-3) ◽  
pp. 279-282 ◽  
Author(s):  
Lorenzo Traldi
Keyword(s):  
Tutte Polynomials

scholarly journals Tutte polynomials of fan-like graphs with applications in benzenoid systems

2021 ◽  
Vol 411 ◽  
pp. 126496
Author(s):  
Tianlong Ma ◽  
Xian’an Jin ◽  
Fuji Zhang
Keyword(s):  
Tutte Polynomials

scholarly journals A study about the Tutte polynomials of benzenoid chains

2017 ◽  
Vol 5 (1) ◽  
pp. 28-32
Author(s):  
Abdulgani Sahin
Keyword(s):  
Tutte Polynomial ◽  
Signed Graphs ◽  
Tutte Polynomials

Abstract The Tutte polynomials for signed graphs were introduced by Kauffman. In 2012, Fath-Tabar, Gholam-Rezaeı and Ashrafı presented a formula for computing Tutte polynomial of a benzenoid chain. From this point on, we have also calculated the Tutte polynomials of signed graphs of benzenoid chains in this study.

scholarly journals Tutte polynomials of generalized parallel connections

2004 ◽  
Vol 32 (1-2) ◽  
pp. 31-43 ◽  
Author(s):  
Joseph Bonin ◽  
Anna de Mier
Keyword(s):  
Tutte Polynomials ◽  
Parallel Connections

scholarly journals An Extension of Matroid Rank Submodularity and the $Z$-Rayleigh Property

10.37236/600 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Arun P. Mani
Keyword(s):  
Half Plane ◽  
Closed Class ◽  
Tutte Polynomials ◽  
A Minor

We define an extension of matroid rank submodularity called $R$-submodularity, and introduce a minor-closed class of matroids called extended submodular matroids that are well-behaved with respect to $R$-submodularity. We apply $R$-submodularity to study a class of matroids with negatively correlated multivariate Tutte polynomials called the $Z$-Rayleigh matroids. First, we show that the class of extended submodular matroids are $Z$-Rayleigh. Second, we characterize a minor-minimal non-$Z$-Rayleigh matroid using its $R$-submodular properties. Lastly, we use $R$-submodularity to show that the Fano and non-Fano matroids (neither of which is extended submodular) are $Z$-Rayleigh, thus giving the first known examples of $Z$-Rayleigh matroids without the half-plane property.

scholarly journals Dichromatic polynomial for graph of a (2,n)-torus knot

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdulgani Şahin
Keyword(s):  
Tutte Polynomial ◽  
Signed Graph ◽  
Torus Knots ◽  
Torus Knot ◽  
Tutte Polynomials ◽  
The Relationship ◽  
Dichromatic Polynomial

AbstractIn this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain the signed graph of a (2,n)-torus knot, marked with {+} signs, via the regular diagram of its. Whereupon, we compute the Tutte polynomial for this graph and find a generalization through these calculations. Finally we obtain dichromatic polynomial lying under the unmarked states of the signed graph of the (2,n)-torus knots by the generalization.

scholarly journals Graph polynomials and symmetries

2019 ◽  
Vol 18 (09) ◽  
pp. 1950172 ◽  
Author(s):  
Nafaa Chbili
Keyword(s):  
Automorphism Group ◽  
Finite Field ◽  
Characteristic Polynomial ◽  
Prime Order ◽  
Tutte Polynomial ◽  
Quotient Graph ◽  
Graph Polynomials ◽  
Tutte Polynomials

In a recent paper, we studied the interaction between the automorphism group of a graph and its Tutte polynomial. More precisely, we proved that certain symmetries of graphs are clearly reflected by their Tutte polynomials. The purpose of this paper is to extend this study to other graph polynomials. In particular, we prove that if a graph [Formula: see text] has a symmetry of prime order [Formula: see text], then its characteristic polynomial, with coefficients in the finite field [Formula: see text], is determined by the characteristic polynomial of its quotient graph [Formula: see text]. Similar results are also proved for some generalization of the Tutte polynomial.

Tutte polynomials of vertex-weighted graphs and group cohomology

2021 ◽  
Vol 207 (2) ◽  
pp. 594-603
Author(s):  
B. S. Bychkov ◽  
A. A. Kazakov ◽  
D. V. Talalaev
Keyword(s):  
Group Cohomology ◽  
Weighted Graphs ◽  
Tutte Polynomials
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