Results 1 to 10 of about 22,632 (241)
Matroid connectivity and singularities of configuration hypersurfaces. [PDF]
Lett Math Phys, 2021 Consider a linear realization of a matroid over a field. One associates with it a configuration polynomial and a symmetric bilinear form with linear homogeneous coefficients.
Denham G, Schulze M, Walther U.
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Matroid Polytopes and their Volumes [PDF]
Discrete and Computational Geometry, 2009 We express the matroid polytope $P_M$ of a matroid $M$ as a signed Minkowski sum of simplices, and obtain a formula for the volume of $P_M$. This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian $Gr_{
Federico Ardila
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Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding [PDF]
Entropy, 2021 In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v
Qi Chen, Minquan Cheng, Baoming Bai
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Generalized Index Coding Problem and Discrete Polymatroids [PDF]
Entropy, 2020 The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids.
Anoop Thomas, Balaji Sundar Rajan
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Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations [PDF]
The Scientific World Journal, 2014 Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as ...
Hui Li, Yanfang Liu, William Zhu
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Flag enumerations of matroid base polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes.
Sangwook Kim
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Relaxations of the matroid axioms I: Independence, Exchange and Circuits [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial ...
Jose ́ Alejandro Samper
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On -connected splitting matroids
AKCE International Journal of Graphs and Combinatorics, 2019 In general, the splitting operation on a binary matroid does not preserve the connectivity of In this paper, we provide sufficient conditions to preserve -connectedness of a binary matroid under splitting operation.
Y.M. Borse, Ganesh Mundhe
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Matroid matching with Dilworth truncation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $H=(V,E)$ be a hypergraph and let $k≥ 1$ and$ l≥ 0$ be fixed integers. Let $\mathcal{M}$ be the matroid with ground-set $E s.t. a$ set $F⊆E$ is independent if and only if each $X⊆V$ with $k|X|-l≥ 0$ spans at most $k|X|-l$ hyperedges of $F$.
Márton Makai
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Journal of Algebraic Combinatorics, 2001 In [Usp. Mat. Nauk 42, No. 2, 107-134 (1987; Zbl 0629.14035), Sov. Math., Dokl. 35, 63-66 (1987); translation from Dokl. Akad. Nauk SSSR 292, 524-528 (1987; Zbl 0645.22005), and Russ. Math. Surv. 42, No. 2, 133-168 (1987; Zbl 0639.14031)] \textit{I. M. Gelfand} and \textit{V. V. Serganova} generalize the notion of matroid to Coxeter matroids.
Vince, Andrew, White, Neil
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