TY - JOUR

T1 - Every finite distributive lattice is isomorphic to the minimizer set of an M♮-concave set function

AU - Fujii, Tomohito

AU - Kijima, Shuji

N1 - Funding Information:
The authors are grateful to Kazuo Murota for his suggestion about the problem, and for his kind advice on their preliminary manuscript. The authors are also grateful to Satoru Fujishige, Akihisa Tamura, Naoyuki Kamiyama and anonymous reviewers for their valuable comments. This work was partly supported by JST PRESTO Grant Number JPMJPR16E4 , Japan.

PY - 2021/1

Y1 - 2021/1

N2 - M♮-concavity is a key concept in discrete convex analysis. For set functions, the class of M♮-concavity is a proper subclass of submodularity. It is a well-known fact that the set of minimizers of a submodular function forms a distributive lattice, where every finite distributive lattice is possible to appear. It is a natural question whether every finite distributive lattice appears as the minimizer set of an M♮-concave set function. This paper affirmatively answers the question.

AB - M♮-concavity is a key concept in discrete convex analysis. For set functions, the class of M♮-concavity is a proper subclass of submodularity. It is a well-known fact that the set of minimizers of a submodular function forms a distributive lattice, where every finite distributive lattice is possible to appear. It is a natural question whether every finite distributive lattice appears as the minimizer set of an M♮-concave set function. This paper affirmatively answers the question.

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U2 - 10.1016/j.orl.2020.10.012

DO - 10.1016/j.orl.2020.10.012

M3 - Article

AN - SCOPUS:85096163095

VL - 49

SP - 1

EP - 4

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 1

ER -