Factoring Groups into Subsets

The factorization theory of abelian groups has a number of applications in the geometry of tilings, coding theory, combinatorics, Fourier analysis, graph theory, and number theory. Focusing on this theory and its interesting applications, this book explores problems in which the underlying factored group is cyclic. The authors consider factorizations of finite cyclic groups that lead to a rich theory with its own techniques and applications. They discuss the problem of tiling the number line with copies of a given tile and factoring finite cyclic groups. The book also presents the theory of variable length codes and certain problems from Fourier analysis where factoring finite cyclic groups plays a prominent part.