Results 111 to 120 of about 22,632 (241)
Bases of G-V Intuitionistic Fuzzy Matroids
Mathematics, 2020 The purpose of this paper is to study intuitionistic fuzzy bases (IFBs) and the intuitive structure of a G−VIFM. Firstly, the intuitionistic fuzzy basis (IFB) of a G−VIFM is defined; then the h-range and properties of an IFB are presented and a necessary
Yonghong Li +4 more
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The Projectivization Matroid of a $q$-Matroid
, 2022 In this paper, we investigate the relation between a $q$-matroid and its associated matroid called the projectivization matroid. The latter arises by projectivizing the groundspace of the $q$-matroid and considering the projective space as the groundset of the associated matroid on which is defined a rank function compatible with that of the $q ...
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New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
wiley +1 more source
On complete classes of valuated matroids [PDF]
TheoretiCSWe characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network.
Edin Husić +3 more
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An Analytic and Probabilistic Approach to the Problem of Matroid Representibility
, 2015 We introduce various quantities that can be defined for an arbitrary matroid, and show that certain conditions on these quantities imply that a matroid is not representable over $\mathbb{F}_q$. Mostly, for a matroid of rank $r$, we examine the proportion
Capodilupo, D. +5 more
core
European Journal of Combinatorics, 2001 20 pages.
Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, U.K. f1 richard.booth@umist.ac.uk f1 f2 alexandre.borovik@umist.ac.uk f2 ( host institution ) +4 more
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Basilica: New canonical decomposition in matching theory
Journal of Graph Theory, Volume 108, Issue 3, Page 508-542, March 2025.Abstract In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are ...
Nanao Kita
wiley +1 more source
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
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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Matroids on the Bases of Simple Matroids
European Journal of Combinatorics, 1981 Let M be a simple matroid (= combinatorial geometry). On the bases of M we consider two matroids S(M, F) and H(M, F), which depend on a field F. S(M, F) is the simplicial matroid with coefficients in F on the bases of M considered as simplices. H(M, F) has been studied by Björner in [1].
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