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Journal of the Ramanujan Mathematical Society

Volume 39, Issue 1, March 2024  pp. 39–53.

On n-color self-inverse compositions

Authors:  R. Sachdeva
Author institution: Department of Mathematics, Guru Nanak Dev University, Amritsar 143 005, India.

Summary:  MacMahon's definition of self-inverse compositions was extended to n-color self-inverse compositions by G. Narang and A. K. Agarwal in 2003. In this paper, we give two different methods of generating n-color self-inverse compositions and their explicit formulas. We also give bijective proofs of their relation with n-color compositions. While enumerating the occurrences of each integer in all n-color self-inverse compositions and n-color compositions, our approach is to describe the various patterns found in this process.

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