| Full text | |
| Author(s): |
da Silva, Robson
;
Hirschhorn, Michael D.
;
Sellers, James A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | DISCRETE MATHEMATICS; v. 345, n. 11, p. 12-pg., 2022-06-10. |
| Abstract | |
In 2007, Andrews and Paule published the eleventh paper in their series on MacMahon's partition analysis, with a particular focus on broken k-diamond partitions. On the way to broken k-diamond partitions, Andrews and Paule introduced the idea of k-elongated partition diamonds. Recently, Andrews and Paule revisited the topic of k-elongated partition diamonds. Using partition analysis and the Omega operator, they proved that the generating function for the partition numbers dk(n) produced by summing the links of k-elongated plane partition diamonds of length n is given by (q2;q2)k >= for each k > 1. (q;q)3k+1 & INFIN; A significant portion of their recent paper involves proving several congruence properties satisfied by d1, d2 and d3, using modular forms as their primary proof tool. In this work, our goal is to extend some of the results proven by Andrews and Paule in their recent paper by proving infinitely many congruence properties satisfied by the functions dk for an infinite set of values of k. The proof techniques employed are all elementary, relying on generating function manipulations and classical q-series results.(c) 2022 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 19/14796-8 - Arithmetic properties of partition functions |
| Grantee: | Robson Oliveira da Silva |
| Support Opportunities: | Regular Research Grants |