Results 11 to 20 of about 6,580 (165)
Advances in Mathematics, 2022 The Tutte polynomial is a well-studied invariant of graphs and matroids. We first extend the Tutte polynomial from graphs to hypergraphs, and more generally from matroids to polymatroids, as a two-variable polynomial. Our definition is related to previous works of Cameron and Fink and of K lm n and Postnikov.
Bernardi, Olivier +2 more
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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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Growing uniform planar maps face by face
Random Structures &Algorithms, Volume 63, Issue 4, Page 942-967, December 2023., 2023 Abstract We provide “growth schemes” for inductively generating uniform random 2p$$ 2p $$‐angulations of the sphere with n$$ n $$ faces, as well as uniform random simple triangulations of the sphere with 2n$$ 2n $$ faces. In the case of 2p$$ 2p $$‐angulations, we provide a way to insert a new face at a random location in a uniform 2p$$ 2p $$‐angulation
Alessandra Caraceni, Alexandre Stauffer
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Renormalization group-like proof of the universality of the Tutte polynomial for matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions
G. Duchamp +3 more
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Geometric bijections between spanning subgraphs and orientations of a graph
Journal of the London Mathematical Society, Volume 108, Issue 3, Page 1082-1120, September 2023., 2023 Abstract Let G$G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy‐to‐describe bijections between spanning trees of G$G$ and (σ,σ∗)$(\sigma ,\sigma ^*)$‐compatible orientations, where the (σ,σ∗)$(\sigma ,\sigma ^*)$‐compatible orientations are the representatives of equivalence classes of orientations
Changxin Ding
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On sufficient conditions for spanning structures in dense graphs
Proceedings of the London Mathematical Society, Volume 127, Issue 3, Page 709-791, September 2023., 2023 Abstract We study structural conditions in dense graphs that guarantee the existence of vertex‐spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and, excluding the bipartite case, contains an odd cycle.
Richard Lang +1 more
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Piperaceae Raddianae: A taxonomic and nomenclatural study of Giuseppe Raddi's Brazilian Piperaceae
TAXON, Volume 72, Issue 4, Page 880-893, August 2023., 2023 Abstract Giuseppe Raddi collected in the state of Rio de Janeiro, Brazil, from November 1817 to June 1818. He published 12 new names in the family Piperaceae in an article that appeared in 1828. Raddi's article has not been cited in specialized literature and these names were never properly studied.
Elsie Franklin Guimarães +3 more
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Computing The Number of Integral Points in4-dimensional Ball Using Tutte Polynomial [PDF]
Engineering and Technology Journal, 2015 In recent years, the uses of high dimensional appear in a large and a lot of applications appearwithin it. So, we study these applications and take one of them that play a central role in the factoring of prime number which is an application especially ...
Shatha Assaad Salman Al-Najjar
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Sampling from the low temperature Potts model through a Markov chain on flows
Random Structures &Algorithms, Volume 62, Issue 1, Page 219-239, January 2023., 2023 Abstract In this article, we consider the algorithmic problem of sampling from the Potts model and computing its partition function at low temperatures. Instead of directly working with spin configurations, we consider the equivalent problem of sampling flows.
Jeroen Huijben, Viresh Patel, Guus Regts
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Stable matching: An integer programming approach
Theoretical Economics, Volume 18, Issue 1, Page 37-63, January 2023., 2023 This paper develops an integer programming approach to two‐sided many‐to‐one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that a stable matching exists in a discrete matching market when the firms' preference profile satisfies a total unimodularity condition that is compatible with ...
Chao Huang
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