Results 1 to 10 of about 14,016 (208)
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
Journal of Algebraic Combinatorics, 2001 In [Usp. Mat. Nauk 42, No. 2, 107-134 (1987; Zbl 0629.14035), Sov. Math., Dokl. 35, 63-66 (1987); translation from Dokl. Akad. Nauk SSSR 292, 524-528 (1987; Zbl 0645.22005), and Russ. Math. Surv. 42, No. 2, 133-168 (1987; Zbl 0639.14031)] \textit{I. M. Gelfand} and \textit{V. V. Serganova} generalize the notion of matroid to Coxeter matroids.
Vince, Andrew, White, Neil
openaire +1 more source
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
doaj +1 more source
Enumerating Matroids and Linear Spaces
Comptes Rendus. Mathématique, 2023 We show that the number of linear spaces on a set of $n$ points and the number of rank-3 matroids on a ground set of size $n$ are both of the form $(cn+o(n))^{n^2/6}$, where $c=e^{\sqrt{3}/2-3}(1+\sqrt{3})/2$.
Kwan, Matthew +2 more
doaj +1 more source
Reducing the rank of a matroid [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider the rank reduction problem for matroids: Given a matroid $M$ and an integer $k$, find a minimum size subset of elements of $M$ whose removal reduces the rank of $M$ by at least $k$. When $M$ is a graphical matroid this problem is the minimum $
Gwenaël Joret, Adrian Vetta
doaj +1 more source
Constructing neighborly polytopes and oriented matroids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 A $d$-polytope $P$ is neighborly if every subset of $\lfloor\frac{d}{2}\rfloor $vertices is a face of $P$. In 1982, Shemer introduced a sewing construction that allows to add a vertex to a neighborly polytope in such a way as to obtain a new neighborly ...
Arnau Padrol
doaj +1 more source