The LP Relaxation Orthogonal Array Polytope and its Permutation Symmetries

TL;DR

This paper investigates the symmetries of the LP relaxation orthogonal array polytope, providing a complete characterization of its permutation symmetry group through theoretical proof and computational verification.

Contribution

It introduces the concept of the LP relaxation orthogonal array polytope and fully characterizes its permutation symmetry group, expanding understanding of symmetries in experimental design.

Findings

Complete symmetry group characterization achieved

Computational verification for multiple cases conducted

Theoretical proof of symmetry group provided

Abstract

Symmetry plays a fundamental role in 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 [6], 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.