Results 11 to 20 of about 4,009 (153)
Active Orders for Matroid Bases
European Journal of Combinatorics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Matroid toric ideals: complete intersection, minors and minimal systems of generators [PDF]
, 2015 In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids $\mathcal M$ such that its corresponding toric ideal $I_{\mathcal M}$ is a complete intersection.
Alfonsín, Jorge Luis Ramírez +1 more
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Counting Bases of Representable Matroids [PDF]
The Electronic Journal of Combinatorics, 2012 We show that it is #P-complete to count the number of bases of matroids representable over a fixed infinite field or fields of fixed characteristic.
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GEOMETRIC BIJECTIONS FOR REGULAR MATROIDS, ZONOTOPES, AND EHRHART THEORY
Forum of Mathematics, Sigma, 2019 Let $M$ be a regular matroid. The Jacobian group $\text{Jac}(M)$ of $M$ is a finite abelian group whose cardinality is equal to the number of bases of $M$.
SPENCER BACKMAN +2 more
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Gröbner Bases of Toric Ideals Associated with Matroids [PDF]
Acta Mathematica Vietnamica, 2022 In 1980, White conjectured that the toric ideal of a matroid is generated by quadratic binomials corresponding to a symmetric exchange. In this paper, we compute Gröbner bases of toric ideals associated with matroids and show that, for every matroid on ground sets of size at most seven except for two matroids, Gröbner bases of toric ideals consist of ...
Hayase, Ken-ichi +3 more
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Power graphs and exchange property for resolving sets
Open Mathematics, 2019 Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given.
Abbas Ghulam +4 more
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Detection of emergent situations in complex systems represented by algebras of transformations
MATEC Web of Conferences, 2016 In this paper we will investigate emergent situations in complex systems represented by algebras of transformations. Though algebras of transformations seem to be rather distanced from a modeled complex system we show that it is representation very ...
Bila Jiri, Novak Martin, Vrba Jan
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Capacity of Spaces of Properties Formulae, Approximations and Qualitative Shapes
Mendel, 2018 This article focuses on the exploration of spaces and models in which we describe the behavior of complex systems as special shapes. We understand these shapes both as a configuration of properties and their values, and on the other, as the formation of ...
Jiri Bila
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Matroid base polytope decomposition
Advances in Applied Mathematics, 2011 23 ...
Chatelain, Vanessa +1 more
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Detection of Emergent Situations in Complex Systems by Structural Invariant (MB, M)
Mendel, 2017 The paper introduces complete description of the detection method that uses structural invariant Matroid and its Bases (MB, M). There are recapitulated essential concepts from the used knowledge field as “complex system, emergent situations (A, B, C ...
Jiri Bila, Martin Novak
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