Results 41 to 50 of about 495 (157)
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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Matroidal frameworks for topological Tutte polynomials [PDF]
, 2018 We introduce the notion of a delta-matroid perspective. A delta-matroid perspective consists of a triple (M,D,N), where M and N are matroids and D is a delta-matroid such that there are strong maps from M to the upper matroid of D and from the lower ...
Moffatt, Iain +3 more
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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.
Michele D'Adderio, Luca Moci
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Evaluating the rank generating function of a graphic 2-polymatroid
, 2006 We consider the complexity of the two-variable rank generating function, $S$, of a graphic 2-polymatroid. For a graph $G$, $S$ is the generating function for the number of subsets of edges of $G$ having a particular size and incident with a particular ...
Noble, SD, Noble, Steven
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The geometry of zonotopal algebras II: Orlik–Terao algebras and Schubert varieties
Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.Abstract Zonotopal algebras, introduced by Postnikov–Shapiro–Shapiro, Ardila–Postnikov, and Holtz–Ron, show up in many different contexts, including approximation theory, representation theory, Donaldson–Thomas theory, and hypertoric geometry. In the first half of this paper, we construct a perfect pairing between the internal zonotopal algebra of a ...
Colin Crowley, Nicholas Proudfoot
wiley +1 more source
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
Crossing estimates for the Ising model on general s‐embeddings
Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.Abstract We prove Russo–Seymour–Welsh‐type crossing estimates for the FK–Ising model on general s‐embeddings whose origami map has an asymptotic Lipschitz constant strictly smaller than 1, provided it satisfies a mild non‐degeneracy assumption. This result extends the work of Chelkak and provides a general framework to prove that the usual connection ...
Rémy Mahfouf
wiley +1 more source
A Convolution Formula for the Tutte Polynomial
Journal of Combinatorial Theory, Series B, 1999 6 ...
Woong Kook +2 more
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Types of embedded graphs and their Tutte polynomials [PDF]
, 2020 We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs on surfaces ...
Moffatt, Iain, Huggett, Stephen
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