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- Title
On the divisibility of 7-elongated plane partition diamonds by powers of 8.
- Authors
Sellers, J. A.; Smoot, N. A.
- Abstract
In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the k -elongated plane partition function d k (n) by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function d 7 (n). We prove that such a congruence family exists — indeed, for powers of 8. The proof utilizes only classical methods, i.e. integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for d k (n) which require more modern methods to prove.
- Subjects
GEOMETRIC congruences; PARTITION functions; DIAMONDS; MODULAR functions; RIEMANN surfaces; DIVISIBILITY groups; CONGRUENCE lattices
- Publication
International Journal of Number Theory, 2024, Vol 20, Issue 1, p267
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042124500131