Results 51 to 60 of about 156 (150)
Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of a matroid $M$ over a commutative ring $R$, assigning to every subset of the ground set an $R$-module according to some axioms. When $R$ is a field, we recover matroids.
Alex Fink, Luca Moci
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The Arithmetic Tutte polynomial of two matrices associated to Trees
Special Matrices, 2018 Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B. +1 more
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Flows on Simplicial Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Given a graph $G$, the number of nowhere-zero $\mathbb{Z}_q$-flows $\phi _G(q)$ is known to be a polynomial in $q$. We extend the definition of nowhere-zero $\mathbb{Z} _q$-flows to simplicial complexes $\Delta$ of dimension greater than one, and prove ...
Matthias Beck, Yvonne Kemper
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Spanning forests in regular planar maps (conference version) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We address the enumeration of $p$-valent planar maps equipped with a spanning forest, with a weight $z$ per face and a weight $u$ per component of the forest.
Mireille Bousquet-Mélou +1 more
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An Interpretation for the Tutte Polynomial
European Journal of Combinatorics, 1999 For a matroid \(M\) which is representable over the rational numbers the author gives a new interpretation of the Tutte polynomial \(T_M(x,y)\) associated to \(M\). The Tutte polynomial \(T_M(x,y)\) of a matroid \(M\) is a or may be the fundamental invariant of \(M\). After its definition by \textit{W. T. Tutte} in 1947 [Proc. Camb. Philos. Soc. 43, 26-
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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
James G. Oxley, Dominic J. A. Welsh
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Bipartition Polynomials, the Ising Model, and Domination in Graphs
Discussiones Mathematicae Graph Theory, 2015 This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph.
Dod Markus +3 more
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Generalized activities and the tutte polynomial
Discrete Mathematics, 1990 This paper examines the Tutte polynomial of a matroid (a generalization of the Tutte's polynomial of graph) from the point of view of basis activities. If \(r(S)\) is the rank of a subset \(S\) of the underlying set \(E\) in a matroid \(M\), then the Tutte polynomial \(t(M;x,y)\) of \(M\) is given by \[ t(M;x,y)=\sum_{S\subseteq E}(x-1)^{r(E)-r(S)}(y ...
Gary Gordon, Lorenzo Traldi
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Chain polynomials and Tutte polynomials
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A tropical approach to rigidity: Counting realisations of frameworks
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract A realisation of a graph in the plane as a bar‐joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely many realisations can be seen as a solution to a system of quadratic equations prescribing the distances between pairs of points.
Oliver Clarke +6 more
wiley +1 more source