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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

The LP Relaxation Orthogonal Array Polytope and its Permutation Symmetries

A.J. Geyer1, D.A. Bulutoglu2, S.J. Rosenberg3
1Air Force Institute of Technology/ENC, 2950 Hobson Way WPAFB, OH 45438-7765.
2Air Force Institute of Technology/ENC, 2950 Hobson Way WPAFB, OH 45433-7765.
3Mathematics and Computer Science Department, University of Wisconsin Superior, Swenson Hall 3023, Belknap and Catlin P.O. Box 2000 Superior, WI 54880.
  • Published: 30/11/2014

Abstract

Symmetry plays a fundamental role in the design of experiments. In particular, symmetries of factorial designs that preserve their statistical properties are exploited to find designs with the best statistical properties. By using a result proved by Rosenberg [1], the concept of the LP relaxation orthogonal array polytope is developed and studied. A complete characterization of the permutation symmetry group of this polytope is made. Also, this characterization is verified computationally for many cases. Finally, a proof is provided.

Keywords: facet; Gaussian elimination; integer linear programming; isometry; linear program; LP relaxation orthogonal array polytope; permutation symmetry group; polytope; recurrence relation; wreath product.
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Citation
A.J. Geyer, D.A. Bulutoglu, S.J. Rosenberg. The LP Relaxation Orthogonal Array Polytope and its Permutation Symmetries[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 091. 165-176. DOI: .