Multicolor compositions and conjugation of N-color compositions

We introduce $n$-multicolor compositions which generalize the $n$-color compositions that Agarwal first defined twenty-two years ago. A summand may bear a set of many integer-valued colors which it bounds from above. We enumerate such multicolored compositions using generating functions. Then we isolate the conjugable class of multicolored compositions known as cracked compositions. A concise exposition of the conjugation of $n$-color compositions is presented in the classical tradition of Percy Alexander MacMahon (1854 - 1929). Our set of conjugable $n$-color compositions turn out to be considerably larger than previously known ones.