Journal of Integer Sequences, Vol. 24 (2021), Article 21.5.6

A Note on the Andrews-Ericksson-Petrov-Romick Bijection for MacMahon's Partition Theorem

Beaullah Mugwangwavari and Darlison Nyirenda
School of Mathematics
University of the Witwatersrand
P. O. Wits 2050
South Africa


Andrews' generalization of MacMahon's partition theorem states that the number of partitions of n in which odd multiplicities are at least 2r + 1 is equal to the number of partitions in which odd parts are congruent to 2r + 1 (mod 4r + 2). In this note, we give a bijective proof of this generalization. Our result naturally extends the bijection of Andrews, Ericksson, Petrov, and Romik for MacMahon's partition theorem.

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Received June 27 2020; revised versions received August 25 2020; April 25 2021. Published in Journal of Integer Sequences, April 25 2021.

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