منابع مشابه
Enumerating bases of self-dual matroids
We define involutively self-dual matroids and prove a relationship between the bases and selfdual bases of these matroids. We use this relationship to prove an enumeration formula for the higher dimensional spanning trees in a class of cell complexes. This gives a new proof of Tutte’s theorem that the number of spanning trees of a central reflex is a perfect square and solves a problem posed by...
متن کاملBASES AND CIRCUITS OF FUZZIFYING MATROIDS
In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...
متن کاملEnumerating Matroids of Fixed Rank
It has been conjectured that asymptotically almost all matroids are sparse paving, i.e. that s(n) ∼ m(n), where m(n) denotes the number of matroids on a fixed groundset of size n, and s(n) the number of sparse paving matroids. In an earlier paper, we showed that log s(n) ∼ logm(n). The bounds that we used for that result were dominated by matroids of rank r ≈ n/2. In this paper we consider the ...
متن کاملRepresenting Small Identically Self-Dual Matroids by Self-Dual Codes
The matroid associated to a linear code is the representable matroid that is defined by the columns of any generator matrix. The matroid associated to a self-dual code is identically self-dual, but it is not known whether every identically self-dual representable matroid can be represented by a self-dual code. This open problem was proposed in [8], where it was proved to be equivalent to an ope...
متن کاملAlgorithms for Enumerating Circuits in Matroids
We present an incremental polynomial-time algorithm for enumerating all circuits of a matroid or, more generally, all minimal spanning sets for a flat. This result implies, in particular, that for a given infeasible system of linear equations, all its maximal feasible subsystems, as well as all minimal infeasible subsystems, can be enumerated in incremental polynomial time. We also show the NP-...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2009
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2008.06.007