Tiling Z(2) with translations of one set
Let A be a finite subset of Z(2). We say A tiles Z(2) with the translation set C, if any integer z is an element of Z(2) can be represented as z(1) + z(2), z(1) is an element of A, z(2) is an element of C in a unique way. In this case we call A a Z(2)- tile and write A circle plus C = Z(2). A tile A is said to be a normal Z(2)-tile if there exists a periodic set C such that A circle plus C = Z(2). We characterize all normal Z(2)- tiles with prime cardinality.
tiling periodicity