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The linear programming relaxation permutation symmetry group of an orthogonal array defining integer linear program

Part of: Polytopes and polyhedra

Published online by Cambridge University Press:  01 June 2016

David M. Arquette  and
Dursun A. Bulutoglu
David M. Arquette
Affiliation:
Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433, USA email David.Arquette@afit.edu
Dursun A. Bulutoglu
Affiliation:
Department of Mathematics and Statistics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433, USA email dursun.bulutoglu@gmail.com

Abstract

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There is always a natural embedding of $S_{s}\wr S_{k}$ into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation with equality constraints. The point of this paper is to prove that in the $2$-level, strength-$1$ case the LP relaxation permutation symmetry group of this formulation is isomorphic to $S_{2}\wr S_{k}$ for all $k$, and in the $2$-level, strength-$2$ case it is isomorphic to $S_{2}^{k}\rtimes S_{k+1}$ for $k\geqslant 4$. The strength-$2$ result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of $S_{2}\wr S_{k}$. We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation.

Supplementary materials are available with this article.

MSC classification

Primary: 52B15: Symmetry properties of polytopes
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 206 - 216
Copyright
© 2016 U.S. Government under licence to the London Mathematical Society, with the exception of the United States of America where no copyright protection exists. 

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