Matroid rank functions and discrete concavity

Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)535-546
Number of pages12
JournalJapan Journal of Industrial and Applied Mathematics
Issue number3
Publication statusPublished - 2012 Oct


  • Combinatorial optimization
  • Discrete concave function
  • Matroid
  • Rank function
  • Submodular function

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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