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On Fuzzy Matroids

Talal Ali AL-Hawary
2012 Zenodo  
Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong maps.  ...  The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C- flats, fuzzy alternative-sets and fuzzy i-flats.  ...  Characterizations of Particular Fuzzy Matroids In this section, we characterize maximal fuzzy matroids, local-flat-fuzzy matroids, free fuzzy matroids and others via fuzzy-regular-flats and fuzzy-c-flats  ... 
doi:10.5281/zenodo.814484 fatcat:3nze4hoh6jfbld632nvyl2j26e

Page 775 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
(JOR-MUT-MS; Al Karak Characterizations of certain matroids via flats. (English summary) J. Autom. Lang. Comb. 7 (2002), no. 3, 295-301.  ...  The aim of the paper is to discuss properties of open-regular-flats, open-feeble-flats, alternative-sets and inner-flats. Some peculiar matroids are characterized via these notions.  ... 

Page 1889 of Mathematical Reviews Vol. , Issue 89D [page]

1989 Mathematical Reviews  
Uniquely K,,,-decomposable graphs are characterized via the existence of an orientation that satisfies certain vertex-degree conditions also on induced subgraphs.  ...  Finally, these techniques are used to characterize the graphs of infinitesimally rigid frameworks on other surfaces, such as the flat torus, the cylinder, cones, etc., using matroid unions of cycle and  ... 

Page 1575 of Mathematical Reviews Vol. 58, Issue 3 [page]

1979 Mathematical Reviews  
Thus in the incidence algebra of flats of G(S), a * {= n, where ¢ is the so-called zeta function (i.e., ((E, F)=1 if ECF and 0 otherwise). One known characterization due to T. J. Brown [J.  ...  He then shows that such an expansion is always possible, defining the free expansion E( f) via its circuits: E(f) is a matroid on the set X = X,, where the disjoint union is indexed over all atoms @ of  ... 

Page 5591 of Mathematical Reviews Vol. , Issue 90J [page]

1990 Mathematical Reviews  
The lattice-theoretic dual L* of the lattice L of flats of a matroid is, in general, no longer a geometric lattice; thus it is not the lattice of flats of a matroid.  ...  A-matroids can be characterized by a generalization of the greedy algorithm. This paper exhibits match- able vertex sets of graphs as A-matroids.  ... 

Cyclic flats of binary matroids

Ragnar Freij-Hollanti, Matthias Grezet, Camilla Hollanti, Thomas Westerbäck
2021 Advances in Applied Mathematics  
Two natural maps from Z(M ) to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterized via their lattice of cyclic flats.  ...  In this paper, first steps are taken towards characterizing rank-decorated lattices of cyclic flats Z(M ) that belong to matroids M that can be represented over a prescribed finite field F q .  ...  Acknowledgments The work of M. Grezet  ... 
doi:10.1016/j.aam.2021.102165 fatcat:3ksgf74irbcxfewrxu5qwkc7la

Hypergraph characterization of split matroids [article]

Kristóf Bérczi, Tamás Király, Tamás Schwarcz, Yutaro Yamaguchi, Yu Yokoi
2022 arXiv   pre-print
We further show that, in contrast to split matroids, the proposed class can be characterized by a single forbidden minor. As an application, we provide a complete list of binary split matroids.  ...  We give a hypergraph characterization of elementary split matroids in terms of independent sets, and show that the proposed class is closed not only under duality and taking minors but also truncation.  ...  In [10] , split matroids were introduced via polyhedral geometry.  ... 
arXiv:2202.04371v1 fatcat:njmqntl5czhchgqwpmjeyigjpy

Exchange properties of combinatorial closure spaces

Ulrich Faigle
1986 Discrete Applied Mathematics  
Finite closure spaces with the Steinitz exchange property are characterized and the connection between the Steinitz and the MacLane exchange property and related exchange properties is discussed.  ...  Introduction It is well-known that matroids may be, equivalently, axiomatized via systems of 'bases' with a certain exchange property or via closure operators with a certain exchange property.  ...  Submodular closure spaces may be characterized by rank functions which generalize matroid rank functions (cf. Faigle [1980] for a general discussion of the associated extension of matroid theory).  ... 
doi:10.1016/0166-218x(86)90046-6 fatcat:x37bspn37nfdjl4hvvrapk377q

Matroids from hypersimplex splits

Michael Joswig, Benjamin Schröter
2017 Journal of combinatorial theory. Series A  
As their key feature these split matroids can be studied via techniques from polyhedral geometry.  ...  A class of matroids is introduced which is very large as it strictly contains all paving matroids as special cases.  ...  Here we give a first characterization of matroid realizability in terms of certain tropical linear spaces (Theorem 31).  ... 
doi:10.1016/j.jcta.2017.05.001 fatcat:62hyxa5u55hqvaxp4xshtrdzsu

Lattice Path Matroids: Structural Properties [article]

Joseph E. Bonin, Anna de Mier
2004 arXiv   pre-print
One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recover the paths that define the matroid.  ...  This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals.  ...  Acknowledgements The authors thank Omer Giménez for some useful observations related to several parts of this paper.  ... 
arXiv:math/0403337v1 fatcat:egukqvy4g5fh3pbopig3thyc7i

Lattice path matroids: Structural properties

Joseph E. Bonin, Anna de Mier
2006 European journal of combinatorics (Print)  
One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recover the paths that define the matroid.  ...  This paper studies structural aspects of lattice path matroids. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats.  ...  Acknowledgement The authors thank Omer Giménez for some useful observations related to several parts of this paper.  ... 
doi:10.1016/j.ejc.2005.01.008 fatcat:tjr27vtcl5d7jjbie343nu62xq

Page 37 of Mathematical Reviews Vol. , Issue 80A [page]

1980 Mathematical Reviews  
Given a finite set § then the matroids on S are paired by duality and there is a certain agreement between restriction and contraction via duality.  ...  An approach to infinite matroids via operators was undertaken by V. Klee [Combi- natorics (Proc. Sympos. Pure Math., Vol. XIX, Univ. California,  ... 

Fundamental polytopes of metric trees via parallel connections of matroids [article]

Emanuele Delucchi, Linard Hoessly
2019 arXiv   pre-print
We tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010.  ...  We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial  ...  Koichi [16] considers lattices of flats L of matroids of linear dependencies of centrally symmetric vector configurations and characterizes the families C ⊆ L \ (max L ) such that the subposet {∧C |  ... 
arXiv:1612.05534v4 fatcat:xsu6fzpbj5f5bjjkdktsm4fnvy

Proto-exact categories of matroids, Hall algebras, and K-theory [article]

Christopher Eppolito, Jaiung Jun, Matt Szczesny
2018 arXiv   pre-print
This paper examines the category Mat_∙ of pointed matroids and strong maps from the point of view of Hall algebras.  ...  We define the algebraic K-theory K_* (Mat_∙) of Mat_∙ via the Waldhausen construction, and show that it is non-trivial, by exhibiting injections π^s_n (S) K_n (Mat_∙) from the stable homotopy groups of  ...  This perspective sheds new light on certain combinatorial Hopf algebras built from matroids, and opens the door to defining algebraic K-theory of matroids.  ... 
arXiv:1805.02281v1 fatcat:vwx4774vlja3flu3ydx5ykqedm

Combinatorially formal arrangements are not determined by their points and lines [article]

Tilman Moeller
2019 arXiv   pre-print
We present an example of a matroid with such a lift but no non-formal realization, thus showing that above condition is not necessary for combinatorial formality.  ...  Formality is not a combinatorial property, raising the question for a characterization for combinatorial formality.  ...  Acknowledgements: The author thanks Michael Falk for helpful discussions regarding the content of this paper.  ... 
arXiv:1903.11925v1 fatcat:zm34dn2ko5bsrggtmtjdyrc3ia
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