Beschreibung:
<jats:p>There is always a natural embedding of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline1" /><jats:tex-math>$S_{s}\wr S_{k}$</jats:tex-math></jats:alternatives></jats:inline-formula> 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 <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline2" /><jats:tex-math>$2$</jats:tex-math></jats:alternatives></jats:inline-formula>-level, strength-<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline3" /><jats:tex-math>$1$</jats:tex-math></jats:alternatives></jats:inline-formula> case the LP relaxation permutation symmetry group of this formulation is isomorphic to <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline4" /><jats:tex-math>$S_{2}\wr S_{k}$</jats:tex-math></jats:alternatives></jats:inline-formula> for all <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline5" /><jats:tex-math>$k$</jats:tex-math></jats:alternatives></jats:inline-formula>, and in the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline6" /><jats:tex-math>$2$</jats:tex-math></jats:alternatives></jats:inline-formula>-level, strength-<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline7" /><jats:tex-math>$2$</jats:tex-math></jats:alternatives></jats:inline-formula> case it is isomorphic to <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline8" /><jats:tex-math>$S_{2}^{k}\rtimes S_{k+1}$</jats:tex-math></jats:alternatives></jats:inline-formula> for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline9" /><jats:tex-math>$k\geqslant 4$</jats:tex-math></jats:alternatives></jats:inline-formula>. The strength-<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline10" /><jats:tex-math>$2$</jats:tex-math></jats:alternatives></jats:inline-formula> result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S1461157016000085_inline11" /><jats:tex-math>$S_{2}\wr S_{k}$</jats:tex-math></jats:alternatives></jats:inline-formula>. We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation.</jats:p><jats:p><jats:uri xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple" xlink:href="http://journals.cambridge.org/sup_S1461157016000085sup001">Supplementary materials are available with this article.</jats:uri></jats:p>