Results 61 to 70 of about 4,266 (227)
Linear Algebraic Relations among Cardinalities of Sets of Matroid Functions
Mathematics, 2023 We introduce a unifying approach for invariants of finite matroids that count mappings to a finite set. The aim of this paper is to show that if the cardinalities of mappings with fixed values on a restricted set satisfy contraction–deletion rules, then ...
Martin Kochol
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Osculating geometry and higher‐order distance Loci
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first‐order tangency. We focus on the data locus of points possessing at least one critical point of the distance function ...
Sandra Di Rocco +2 more
wiley +1 more source
, 1965 This work is based on a series of papers in the Transactions of the American Mathematical Society: A homotopy theorem for matroids, I and II, 88, 144-174 (1958); and Matroids and graphs, 90, 572-552 (1959). These papers set out a theory of matroids, with
Tutte, W. T.
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, 2022 Matroids over tracts provide an algebraic framework simultaneously generalizing the notions of matroids, oriented matroids, and valuated matroids, presented by Baker and Bowler.
Su, Ting
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Base Axioms of Modular Supermatroids
Journal of Applied Mathematics, 2014 This paper studies axiom systems of supermatroids. Barnabei et al.'s base axioms concerning poset matroids (i.e., distributive supermatroids) are generalized to modular supermatroids, and a mistake in the proof of base axioms of poset matroids is pointed
Xiaonan Li, Sanyang Liu
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The multivariate arithmetic Tutte polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two.
Petter Brändèn, Luca Moci
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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
Single-element extensions of matroids
, 1965 Extensions of matroids to sets containing one additional element are characterized in terms of modular cuts of the lattice of closed subsets. An equivalent characterization is given in terms of linear subclasses or the set or circuits or bonds of the ...
Crapo, Henry H.
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Duality, Matroids, Qubits, Twistors, and Surreal Numbers
Frontiers in Physics, 2018 We show that via the Grassmann-Plücker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors, and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be
J. A. Nieto
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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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