Combinatorics of n-Colored Cyclic Compositions

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