Results 11 to 20 of about 4,343 (225)
The Projectivization Matroid of a $q$-Matroid
CoRR, 2022 In this paper, we investigate the relation between a $q$-matroid and its associated matroid called the projectivization matroid. The latter arises by projectivizing the groundspace of the $q$-matroid and considering the projective space as the groundset ...
Jany, Benjamin
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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 +2 more
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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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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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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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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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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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SIAM Journal on Discrete Mathematics, 2023 For all positive integers $s$ and $t$ exceeding one, a matroid $M$ on $n$ elements is {\em nearly $(s, t)$-cyclic} if there is a cyclic ordering $σ$ of its ground set such that every $s-1$ consecutive elements of $σ$ are contained in an $s$-element circuit and every $t-1$ consecutive elements of $σ$ are contained in a $t$-element cocircuit. In the case
Nick Brettell +2 more
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