Results 71 to 80 of about 4,009 (153)
Naval Research Logistics (NRL), Volume 72, Issue 1, Page 133-147, February 2025.Abstract A classic result of Korte and Hausmann [1978] and Jenkyns [1976] bounds the quality of the greedy solution to the problem of finding a maximum value basis of an independence system (E,ℐ)$$ \left(E,\mathcal{I}\right) $$ in terms of the rank‐quotient. We extend this result in two ways.
Sven de Vries +2 more
wiley +1 more source
The category of a partitioned fan
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract In this paper the notion of an admissible partition of a simplicial polyhedral fan is introduced and the category of a partitioned fan is defined as a generalisation of the τ$\tau$‐cluster morphism category of a finite‐dimensional algebra. This establishes a complete lattice of categories around the τ$\tau$‐cluster morphism category, which is ...
Maximilian Kaipel
wiley +1 more source
Rough matroids based on coverings
, 2013 The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy.
Yang, Bin, Zhao, Hong, Zhu, William
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Chow rings of matroids as permutation representations
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincaré duality and the Hard Lefschetz theorem.
Robert Angarone +2 more
wiley +1 more source
An extended abstract of this paper appears in the proceedings of ESA ...
Bentert, Matthias +3 more
openaire +3 more sources
Problems on Group-Labeled Matroid Bases
Consider a matroid equipped with a labeling of its ground set to an abelian group. We define the label of a subset of the ground set as the sum of the labels of its elements. We study a collection of problems on finding bases and common bases of matroids with restrictions on their labels.
Hörsch, Florian +4 more
openaire +4 more sources
Discrete MathematicsIn this work, we explore the application of modulus in matroid theory, specifically, the modulus of the family of bases of matroids. This study not only recovers various concepts in matroid theory, including the strength, fractional arboricity, and principal partitions, but also offers new insights.
Huy Truong, Pietro Poggi-Corradini
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Bases for permutation groups and matroids
European Journal of Combinatorics, 1995 If \(G\) is a permutation group acting on an \(n\)-set \(X\), then the bases of \(G\) are the sets of points of \(X\) that are (pointwise) fixed only by the identity of \(G\) (i.e., the sets with trivial stabilizer). An irredundant basis is an ordered basis such that no element is fixed by the joint stabilizer of the previous elements. It is shown that
Cameron, P.J, Fon-Der-Flaass, D.G
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Sample-Based Matroid Prophet Inequalities
Proceedings of the 25th ACM Conference on Economics and ComputationWe study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a sublinear number of samples was known for general matroids.
Hu Fu +5 more
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On the Congruency-Constrained Matroid Base
Consider a matroid where all elements are labeled with an element in $\mathbb{Z}$. We are interested in finding a base where the sum of the labels is congruent to $g \pmod m$. We show that this problem can be solved in $\tilde{O}(2^{4m} n r^{5/6})$ time for a matroid with $n$ elements and rank $r$, when $m$ is either the product of two primes or a ...
Siyue Liu, Chao Xu
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