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Journal of the Ramanujan Mathematical Society

Volume 38, Issue 1, March 2023  pp. 57–69.

N-multicolor partitions of numbers

Authors:  A. M. Alanazi, A. O. Munagi and D. Nyirenda
Author institution: Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

Summary:  An n-multicolor partition is a colored partition of a positive integer in which a summand m may bear more than one color simultaneously, given that the maximal color is bounded above by m. These objects generalize the n-color partitions. We obtain many enumeration results using generating functions and bijective proofs. We also prove combinatorial identities, and obtain arithmetic congruences satisfied by the numbers of certain classes of n-multicolor partitions.

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