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.
|ジャーナル||Japan Journal of Industrial and Applied Mathematics|
|出版ステータス||Published - 2012 10月|
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