Results 1 to 10 of about 266 (116)
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_{
Carolina Benedetti +2 more
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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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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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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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Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization
Discrete Analysis, 2022 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization, Discrete Analysis 2022:3, 32 pp. As its title suggests, this paper follows on from the previous paper published in this journal.
Katie Clinch +2 more
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Weighted Tree-Numbers of Matroid Complexes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights.
Woong Kook, Kang-Ju Lee
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A new matroid constructed by the rank function of a matroid
AKCE International Journal of Graphs and Combinatorics, 2020 In this article, we construct a submodular function using the rank function of a matroid and study induced matroid with constructed polymatroid, then we relate some properties of connectivity of new matroid with the main matroid.
Moein Pourbaba +2 more
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