Results 61 to 70 of about 3,648 (134)
Aequationes Mathematicae, 1969 $q$-Matroids are defined on complemented modular support lattices. Minors of length 2 are of four types as in a "classical" matroid. Tutte polynomials $\tau(x,y)$ of matroids are calculated either by recursion over deletion/contraction of single elements, by an enumeration of bases with respect to internal/external activities, or by substitution $x \to
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Valuative invariants for large classes of matroids
Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
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Interlace polynomials and Tutte polynomials
, 2013 This article has been superseded by arXiv:1301 ...
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Tutte polynomials and G-parking functions
Advances in Applied Mathematics, 2010 Let $G$ be a connected graph with vertex set $\{0,1,2,...,n\}$. We allow $G$ to have multiple edges and loops. In this paper, we give a characterization of external activity by some parameters of $G$-parking functions. In particular, we give the definition of the bridge vertex of a $G$-parking function and obtain an expression of the Tutte polynomial ...
Chang, Hungyung, Ma, Jun, Yeh, Yeong-Nan
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Mesh Parameterization Meets Intrinsic Triangulations
Computer Graphics Forum, Volume 43, Issue 5, August 2024.Abstract A parameterization of a triangle mesh is a realization in the plane so that all triangles have positive signed area. Triangle mesh parameterizations are commonly computed by minimizing a distortion energy, measuring the distortions of the triangles as they are mapped into the parameter domain.
Koray Akalin +3 more
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From the Ising and Potts models to the general graph homomorphism polynomial
, 2015 In this note we study some of the properties of the generating polynomial for homomorphisms from a graph to at complete weighted graph on $q$ vertices.
Markström, Klas
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European Journal of CombinatoricsThe classical Tutte polynomial is a two-variate polynomial $T_G(x,y)$ associated to graphs or more generally, matroids. In this paper, we introduce a polynomial $\widetilde{T}_H(x,y)$ associated to a bipartite graph $H$ that we call the permutation Tutte polynomial of the graph $H$.
Beke, Csongor +3 more
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Tutte polynomials computable in polynomial time
Discrete Mathematics, 1992 Determining the Tutte polynomial of a matroid at a fixed point \(P\) of the plane is known to be \(\# P\)-hard unless \(P\) lies on a certain hyperbola or is one of 8 special points (\textit{F. Jaeger}, \textit{D. L. Vertigan} and the second author [Math. Proc. Camb. Philos. Soc. 108, No. 1, 35-53 (1990; Zbl 0747.57006)]). The authors show that for any
Oxley, J.G., Welsh, D.J.A.
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Ehrhart polynomial and arithmetic Tutte polynomial
European Journal of Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D'ADDERIO M, MOCI L
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Graph polynomials and statistical physics [PDF]
, 2007 Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.Includes bibliographical references (p. 53-54).We present several graph polynomials, of which the most important one is the Tutte polynomial.
Kim, Jae Ill, S.M. Massachusetts Institute of Technology
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