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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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Fractional dynamic system simulating the growth of microbe [PDF]
Advances in Difference Equations, 2021 There are different approaches that indicate the dynamic of the growth of microbe. In this research, we simulate the growth by utilizing the concept of fractional calculus.
Samir B. Hadid, Rabha W. Ibrahim
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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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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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Evaluations of topological Tutte polynomials [PDF]
Combinatorics, Probability and Computing, 2014 We find new properties of the topological transition polynomial of embedded graphs, $Q(G)$. We use these properties to explain the striking similarities between certain evaluations of Bollob\'as and Riordan's ribbon graph polynomial, $R(G)$, and the ...
Aigner +6 more
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The multivariate arithmetic Tutte polynomial [PDF]
Transactions of the American Mathematical Society, 2012 We introduce an arithmetic version of the multivariate Tutte polynomial, and (for representable arithmetic matroids) a quasi-polynomial that interpolates between the two.
Brändén, Petter, Moci, Luca
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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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Graph polynomials associated with Dyson-Schwinger equations [PDF]
Mathematica Moravica, 2023 Quantum motions are encoded by a particular family of recursive Hochschild equations in the renormalization Hopf algebra which represent Dyson-Schwinger equations, combinatorially.
Shojaei-Fard Ali
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Relaxations of the matroid axioms I: Independence, Exchange and Circuits [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial ...
Jose ́ Alejandro Samper
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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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