Results 11 to 20 of about 335 (183)
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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On the correlation gap of matroids. [PDF]
Math Program, 2023 Abstract A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms and mechanism design settings.
Husić E, Koh ZK, Loho G, Végh LA.
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The Category of Matroids [PDF]
Applied Categorical Structures, 2017 31 pages, 10 diagrams, 28 ...
Chris Heunen, Vaia Patta
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Matroids, delta-matroids and embedded graphs [PDF]
Journal of Combinatorial Theory, Series A, 2019 v2: We have split this paper into two. The later material of version 1 now appears in "On the interplay between embedded graphs and delta-matroids".
Carolyn Chun +3 more
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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 of the associated matroid on which is defined a rank function compatible with that of the $q ...
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On n-connected minors of the es-splitting binary matroids
Electronic Journal of Graph Theory and Applications, 2021 The es-splitting operation on an n-connected binary matroid may not yield an n-connected matroid for (n ≥ 3). In this paper, we show that given an n-connected binary matroid M of rank r, the resulting es-splitting binary matroid has an n-connected minor ...
Prashant Pralhad Malavadkar +2 more
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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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Generalized permutohedra, h-vectors of cotransversal matroids and pure O-sequences (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Stanley has conjectured that the h-vector of a matroid complex is a pure O-sequence. We will prove this for cotransversal matroids by using generalized permutohedra. We construct a bijection between lattice points inside a $r$-dimensional convex polytope
Suho Oh
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Kazhdan-Lusztig polynomials of fan matroids, wheel matroids, and whirl matroids
Journal of Combinatorial Theory, Series A, 2022 60 pages, 15 ...
Linyuan Lu +2 more
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Matroids related to groups and semigroups
Researches in Mathematics, 2023 Matroid is defined as a pair $(X,\mathcal{I})$, where $X$ is a nonempty finite set, and $\mathcal{I}$ is a nonempty set of subsets of $X$ that satisfies the Hereditary Axiom and the Augmentation Axiom.
D.I. Bezushchak
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