Combinatorics of n-color cyclic compositions

Integer compositions and related enumeration problems have been of interest to combinatorialists and number theorists for a long time. The cyclic and colored analogues of this concept, although interesting, have not been extensively studied. In this paper we explore the combinatorics of $n$-color cyclic compositions, presenting generating functions, bijections, asymptotic formulas related to the number of such compositions, the number of parts, and the number of restricted parts.