منابع مشابه
Rank functions of strict cg-matroids
A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by S. Fujishige, G. A. Koshevoy, and Y. Sano in [9]. A cg-matroid whose rank function is naturally defined is called a strict cg-matroid. In this paper, we give characterizations of strict cg-matroids by their rank functions.
متن کاملThe greedy algorithm for strict cg-matroids
A matroid-like structure defined on a convex geometry, called a cg-matroid, is defined by S. Fujishige, G. A. Koshevoy, and Y. Sano in [6]. Strict cg-matroids are the special subclass of cg-matroids. In this paper, we show that the greedy algorithm works for strict cg-matroids with natural weightings, and also show that the greedy algorithm works for a hereditary system on a convex geometry wit...
متن کاملOn the rank functions of H-matroids
The notion of H-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of H-matroids by the greedy algorithm. In this note, we give a characterization of some H-matroids by rank functions. 2010 MSC: 05B35, 90C27
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We consider matroidal structures on convex geometries, which we call cg-matroids. The concept of a cg-matroid is closely related to but different from that of a supermatroid introduced by Dunstan, Ingleton, and Welsh in 1972. Distributive supermatroids or poset matroids are supermatroids defined on distributive lattices or sets of order ideals of posets. The class of cg-matroids includes distri...
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 ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.08.095