MacMahon's Double Vision: Partition Diamonds Revisited
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915364394237952 |
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| author | Beck, Matthias Wijesekera, Kobe |
| author_facet | Beck, Matthias Wijesekera, Kobe |
| contents | Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's $Ω$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MacMahon's Double Vision: Partition Diamonds Revisited Beck, Matthias Wijesekera, Kobe Combinatorics Plane partition diamonds were introduced by Andrews, Paule, and Riese (2001) as part of their study of MacMahon's $Ω$-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. |
| title | MacMahon's Double Vision: Partition Diamonds Revisited |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.23354 |