On Some n-Color Composition

Abstract

In this thesis, we studied ordered partitions, called compositions which were first defined by MacMahon, ``P.A MacMahon, Combinatory Analysis, AMS Chelsea Publishing, 2001." Chapter 1 is devoted to basic definitions and preliminary results on classical partitions, compositions and Fibonacci numbers. Chapter 2 discuss the generating functions of n-Color Compositions and some recurrence formulas related to compositions. In Chapter 3, we have studied an identity analouges to Euler's partition identity and some new combinatorial properties of n-color compositions.