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dc.contributor.authorKohl, Florian
dc.contributor.authorLi, Yanxi
dc.contributor.authorRauh, Johannes
dc.contributor.authorYoshida, Ruriko
dc.date.accessioned2018-08-08T22:52:05Z
dc.date.available2018-08-08T22:52:05Z
dc.date.issued2017
dc.identifier.urihttp://hdl.handle.net/10945/59421
dc.descriptionThe software is available at http://ehrhart.math.fu-berlin.de/People/fkohl/HASE/.en_US
dc.description.abstractThe question whether there exists an integral solution to the system of linear equations with non-negativity constraints, Ax = b, x ≥ 0, where A ∈ Zm×n and b ∈ Zm, finds its applications in many areas such as oper- ations research, number theory, combinatorics, and statistics. In order to solve this problem, we have to understand the semigroup generated by the columns of the matrix A and the structure of the “holes” which are the dif- ference between the semigroup and its saturation. In this paper, we discuss the implementation of an algorithm by Hemmecke, Takemura, and Yoshida that computes the set of holes of a semigroup and we discuss applications to problems in combinatorics. Moreover, we compute the set of holes for the common diagonal effect model and we show that the nth linear ordering polytope has the integer-decomposition property for n ≤ 7.en_US
dc.publisherArXiven_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleSemigroups -- A Computational Approachen_US
dc.typeArticleen_US
dc.contributor.departmentOperations Research (OR)


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