Geodesic
A refinement of and a companion to MacMahon's partition identity
Matthew Russell1
1Texas A&M University
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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We provide a refinement of MacMahon's partition identity on sequence-avoiding partitions, and use it to produce another mod 6 partition identity. In addition, we show that our technique also extends to cover Andrews's generalization of MacMahon's identity. Our proofs are bijective in nature, exploiting a theorem of Xiong and Keith.
DOI : 10.37236/12301
Classification : 05A17, 11P81, 11P83, 05A15
Mots-clés : \(m\)-length type of a partition, conjugates of partitions

Matthew Russell  1

1 Texas A&M University 
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Matthew Russell. A refinement of and a companion to MacMahon's partition identity. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/12301

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