Primary classes of n-color compositions - enumerations and combinatorial connections

Abstract

The study of compositions was initiated by MacMahon in 1893, and later extended to n-color compositions by Agarwal in 2000. In this dissertation we study standard compositions and n-color composition enumerations. Combinatorial proofs are studied using the graphical representation of compositions and n-color compositions with restricted parts. We also consider bounded part and color sizes of n-color com-positions, and explore interesting combinatorial links and conclusions. The shape of n-color compositions was introduced by Munagi, where he dealt with general compositions. Here we establish the link between the Fibonacci sequence and restricted compositions, classified by part size and color size, by providing enumerative proofs