From More-Part Sperner Problems to Mixed Orthogonal Arrays

Eva Czabarka

Sperner's theorem states that the largest antichain in the subset lattice of a finite set is (one of the) largest levels. Since this theorem a plethora of Sperner type problems have been proposed. Mixed orthogonal arrays are used in design of experiments, coding theory and many other areas. We found an unexpected connection between Sperner-type problems and mixed orthogonal arrays. We have explored this connection, proved an LYM-type inequality for more-part Sperner systems and multi-systems, and created new mixed orthogonal arrays using only simple rounding.

This is joint work in part with H.K. Aydinian, K. Engel, P.L. Erd\H{o}s and L.A. Sz\'{e}kely.