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The multivariate arithmetic Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two.
Petter Brändèn, Luca Moci
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Computing Tutte Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable.
Michael Monagan
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Modifications of Tutte–Grothendieck invariants and Tutte polynomials [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Generalized Tutte–Grothendieck invariants are mappings from the class of matroids to a commutative ring that are characterized recursively by contraction–deletion rules. Well known examples are Tutte, chromatic, tension and flow polynomials.
Martin Kochol
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Simulating quantum computations with Tutte polynomials [PDF]
npj Quantum Information, 2021 We establish a classical heuristic algorithm for exactly computing quantum probability amplitudes. Our algorithm is based on mapping output probability amplitudes of quantum circuits to evaluations of the Tutte polynomial of graphic matroids.
Ryan L. Mann
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A Tutte polynomial for toric arrangements [PDF]
Transactions of the American Mathematical Society, 2010 We introduce a multiplicity Tutte polynomial M(x,y), with applications to zonotopes and toric arrangements. We prove that M(x,y) satisfies a deletion-restriction recurrence and has positive coefficients.
Ad Alessandro Pucci, Luca Moci
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Dirac traces and the Tutte polynomial
Journal of High Energy PhysicsPerturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the ...
Joshua Lin
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A lattice point counting generalisation of the Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion- contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a matroid, and in fact
Amanda Cameron, Alex Fink
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Fourientation activities and the Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it.
Spencer Backman +2 more
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The arithmetic Tutte polynomials of the classical root systems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the
Federico Ardila +2 more
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On the evaluation of the Tutte polynomial at the points (1,-1) and (2,-1) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 C. Merino [Electron. J. Combin. 15 (2008)] showed that the Tutte polynomial of a complete graph satisfies $t(K_{n+2};2,-1)=t(K_n;1,-1)$. We first give a bijective proof of this identity based on the relationship between the Tutte polynomial and the ...
Andrew Goodall +3 more
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