Some explicit constructions of ternary non-full-rank tilings of abelian groups

A tiling of a finite abelian group G is a pair (A,B) of subsets of G, such that both A and B contain the identity element e of G and every g ∈ G can be uniquely written in the form g = ab, where a ∈ A and b ∈ B. A tiling (A,B) of G is called full-rank if hAi = hB >= G, Otherwise, it is called a non-full rank tiling. In this paper, we show some explicit constructions of non-full rank tilings of 3−groups of order 3^4. https://doi.org/10.28919/jmcs/3217