Results 21 to 30 of about 4,343 (225)
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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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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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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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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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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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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