Matroid rank functions and discrete concavity
نویسنده
چکیده
We discuss the relationship between matroid rank functions and a concept of discrete concavity called M-concavity. It is known that a matroid rank function and its weighted version called a weighted rank function are M-concave functions, while the (weighted) sum of matroid rank functions is not M-concave in general. We present a sufficient condition for a weighted sum of matroid rank functions to be an M-concave function, and show that every weighted rank function can be represented as a weighted sum of matroid rank functions satisfying this condition.
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.
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