Results 1 to 10 of about 275 (182)
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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Entropic Matroids and Their Representation [PDF]
Entropy, 2019 This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p.
Emmanuel Abbe, Sophie Spirkl
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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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Matroids on convex geometries (cg-matroids)
Discrete Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Satoru Fujishige, Yoshio Sano
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Approximate‐Guided Representation Learning in Vision Transformer
CAAI Transactions on Intelligence TechnologyIn recent years, the transformer model has demonstrated excellent performance in computer vision (CV) applications. The key lies in its guided representation attention mechanism, which uses dot‐product to depict complex feature relationships, and ...
Kaili Wang +4 more
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On a Unimodality Conjecture in Matroid Theory [PDF]
Discrete Mathematics & Theoretical Computer Science, 2002 A certain unimodal conjecture in matroid theory states the number of rank- r matroids on a set of size n is unimodal in r and attains its maximum at r=⌊ n/2 ⌋.
W. M. B. Dukes
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Non-representable hyperbolic matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. Hyperbolic polynomials give rise to a class of (hyperbolic) matroids which properly contains the class of matroids ...
Nima Amini, Petter Branden
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Discrete Mathematics & Theoretical Computer Science, 2013 We introduce the notion of a matroid $M$ over a commutative ring $R$, assigning to every subset of the ground set an $R$-module according to some axioms. When $R$ is a field, we recover matroids.
Alex Fink, Luca Moci
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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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Connected Degree of Fuzzifying Matroids
Journal of Mathematics, 2022 Polya’s plausible reasoning methods are crucial not only in discovery of mathematics results, modeling methods, and data processing methods but also in many practical problems’ solving.
Xiu Xin +4 more
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