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arXiv · 2506.23354

MacMahon's Double Vision: Partition Diamonds Revisited

Matthias Beck·Kobe Wijesekera
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Abstract

Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's $\Omega$-operator in search for integer partition identities. More recently, Dockery, Jameson, Sellers, and Wilson (2024) extended this concept to $d$-fold partition diamonds and found their generating function in a recursive form. We approach $d$-fold partition diamonds via Stanley's (1972) theory of $P$-partitions and give a closed formula for a bivariate generalization of the Dockery--Jameson--Sellers--Wilson generating function; its main ingredient is the Euler--Mahonian polynomial encoding descent statistics of permutations.

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Matthias Beck, Kobe Wijesekera. 2025-06-29. MacMahon's Double Vision: Partition Diamonds Revisited. https://arxiv.org/abs/2506.23354

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