The Second Order of Reflection Operators on Circular Sequences

Abstract

This research extend the idea from the work of Alon, Krasikov and Peres which investigate calculating the numbers of reflection operators on an arbitrary circular sequences. This is a generalization of a problem in International Mathematical Olympiad. In this work, we develop an idea of the first order reflection operators to be a new reflection operation which are called the second order of reflection operators. The reflection operations induce the complicate of calculating the numbers of its more than above. Finally, we introduce the numbers of the second order of reflection operators on an arbitrary circular sequences.