Normalized difference set tiling conjecture

A difference set tiling in a group is a collection of its Q2 ( , , ) difference sets that partition ⧵ {; ; 1}; ; . It can exist in an abelian as well as in a nonabelian group. A tiling is normalized if a product of elements in each difference set equals 1. All known cases in abelian groups are normalized. Ćustić, Krčadinac, and Zhou made a conjecture that this is necessary. We will call it a normalized tiling conjecture (NTC). Using character theory, we prove that NTC is true for ( , , 1) where is odd. Also, if ( , , ) difference set has a multiplier, we prove that NTC is also true.