On Extending Closure Systems to Matroids
نویسندگان
چکیده
منابع مشابه
CHARACTERIZATION OF L-FUZZIFYING MATROIDS BY L-FUZZIFYING CLOSURE OPERATORS
An L-fuzzifying matroid is a pair (E, I), where I is a map from2E to L satisfying three axioms. In this paper, the notion of closure operatorsin matroid theory is generalized to an L-fuzzy setting and called L-fuzzifyingclosure operators. It is proved that there exists a one-to-one correspondencebetween L-fuzzifying matroids and their L-fuzzifying closure operators.
متن کاملM-FUZZIFYING MATROIDS INDUCED BY M-FUZZIFYING CLOSURE OPERATORS
In this paper, the notion of closure operators of matroids is generalized to fuzzy setting which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...
متن کاملFrom torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
متن کاملcharacterization of l-fuzzifying matroids by l-fuzzifying closure operators
an l-fuzzifying matroid is a pair (e, i), where i is a map from2e to l satisfying three axioms. in this paper, the notion of closure operatorsin matroid theory is generalized to an l-fuzzy setting and called l-fuzzifyingclosure operators. it is proved that there exists a one-to-one correspondencebetween l-fuzzifying matroids and their l-fuzzifying closure operators.
متن کاملExtending -systems to bases of root systems
Let R be an indecomposable root system. It is well known that any root is part of a basis B of R. But when can you extend a set of two or more roots to a basis B of R? A -system is a linearly independent set of roots, C , such that if ̨ and ˇ are in C , then ̨ ˇ is not a root. We will use results of Dynkin and Bourbaki to show that with two exceptions, A3 Bn and A7 E8, an indecomposable -system...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2002
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0423