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

There is always a natural embedding of S_s~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_s~S_k for all k, and in the 2-level, strength-2 case it is isomorphic to S₂^k~S_k+1 for k≥4. The strength-2 result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of S₂~S_k. We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation. [ABSTRACT FROM AUTHOR]