|
Proofs of some conjectures of Andrews and Paule on 2-elongated plane partitions |
Proofs of some conjectures of Andrews and Paule on 2-elongated plane partitions |
Received:January 03, 2024 Revised:May 09, 2024 |
DOI: |
中文关键词: |
英文关键词:partitions, congruences, 2-elongated plane partitions, theta function identities |
基金项目: |
|
Hits: 70 |
Download times: 0 |
中文摘要: |
|
英文摘要: |
Recently, Andrews and Paule established the generating functions for the $k$-elongated plane partition function $d_k(n)$
and proved a large number of results on $d_k(n)$ with $k=2,3$. In particular, they posed some conjectures on
congruences modulo powers of 3 for $d_2(n)$. Their work has attracted the attention of Hirschhorn, Sellers, Silva and Smoot.
Very recently, Smoot proved a congruence family for $d_2(n)$ which implies one conjecture due to Andrews and Paule by using
the localization method. In this paper, we prove the rest two conjectures given by Andrew and Paule. |
View/Add Comment Download reader |
|
|
|