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There is always a natural embedding of Ss~Sk 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 Ss~Sk for all k, and in the 2-level, strength-2 case it is isomorphic to S2k~Sk+1 for k≥4. The strength-2 result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of S2~Sk. We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]