Simpler exchange axioms for M-concave functions on generalized polymatroids

  • Kazuo Murota
  • Akiyoshi ShiouraEmail author
Original Paper Area 3


\({\mathrm{M}}^\natural \)-concave functions form a class of discrete concave functions in discrete convex analysis, and are defined by a certain exchange axiom. We show in this paper that \({\mathrm{M}}^\natural \)-concave functions can be characterized by a combination of two simpler exchange properties. It is also shown that for a function defined on an integral polymatroid, a much simpler exchange axiom characterizes \({\mathrm{M}}^\natural \)-concavity. These results have some significant implications in discrete convex analysis.


Discrete convex analysis Discrete optimization Polymatroid Exchange property 

Mathematics Subject Classification

90C27 52B40 



The authors thank Yu Yokoi and the anonymous referees for their valuable comments on the manuscript.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Business AdministrationTokyo Metropolitan UniversityTokyoJapan
  2. 2.Department of Industrial Engineering and EconomicsTokyo Institute of TechnologyTokyoJapan

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