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A Note on the Andrews-Ericksson-Petrov-Romick Bijection for MacMahon's Partition Theorem
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Beaullah Mugwangwavari and Darlison Nyirenda

School of Mathematics

University of the Witwatersrand

P. O. Wits 2050

Johannesburg

South Africa

**Abstract:**

Andrews' generalization of MacMahon's partition theorem states that
the number of partitions of *n* in which odd multiplicities are at
least 2*r* + 1 is equal to the number of partitions in which odd
parts are congruent to 2*r* + 1 (mod 4*r* + 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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