Results 1 to 10 of about 9,755 (179)
Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design, and Coding [PDF]
Entropy, 2021 In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v
Qi Chen, Minquan Cheng, Baoming Bai
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A Vector Matroid-Theoretic Approach in the Study of Structural Controllability Over F(z) [PDF]
IEEE Access, 2017 In this paper, the structural controllability of the systems over F(z) is studied using a new mathematical method-matroids. First, a vector matroid is defined over F(z). Second, the full rank conditions of [sI - A|B](s ∈ p) are derived in terms of
Yupeng Yuan +4 more
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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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Matroid Polytopes and Their Volumes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We express the matroid polytope $P_M$ of a matroid $M$ as a signed Minkowski sum of simplices, and obtain a formula for the volume of $P_M$. This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian $Gr_{
Federico Ardila +2 more
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K-classes for matroids and equivariant localization [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial.
Alex Fink, David Speyer
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Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations [PDF]
The Scientific World Journal, 2014 Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as ...
Hui Li, Yanfang Liu, William Zhu
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Relaxations of the matroid axioms I: Independence, Exchange and Circuits [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial ...
Jose ́ Alejandro Samper
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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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On the Optimality of Linear Index Coding Over the Fields With Characteristic Three
IEEE Open Journal of the Communications Society, 2022 It has been known that the insufficiency of linear coding in achieving the optimal rate of the general index coding problem is rooted in its rate’s dependency on the field size. However, this dependency has been described only through the two well-
Arman Sharififar +2 more
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Interpolation, box splines, and lattice points in zonotopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Given a finite list of vectors $X \subseteq \mathbb{R}^d$, one can define the box spline $B_X$. Box splines are piecewise polynomial functions that are used in approximation theory. They are also interesting from a combinatorial point of view and many of
Matthias Lenz
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