Arithmetic density and new congruences for 3 -core partitions
Article Type
Research Article
Publication Title
Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Abstract
A partition of n is called a t-core partition if none of its hook number is a multiple of t. In 2019, Hirschhorn and Sellers (Bull. Austral. Math. Soc. 1 (2019) 51–55) proved a parity result for 3-core partitions a3(n) . In this article, we prove density results for a3(n) , that is, a3(n) is almost always divisible by an arbitrary power of 2 and 3. Further, by using a result of Ono and Taguchi (Int. J. Number Theory 1 (2005) 75–101) on nilpotency of Hecke operators, we deduce that a3(n) is divisible by arbitrary powers of 2. Moreover, by employing Radu and Sellers approach (Int. J. Number Theory 7 (2011) 2249–2259), we obtain an algorithm and new congruences modulo 3 for a3(n) . Furthermore, by applying dissection formulas, we obtain new infinite families of Ramanujan type congruences for a3(n) which are divisible by 2.
DOI
https://10.1007/s12044-023-00751-5
Publication Date
12-1-2023
Recommended Citation
Jindal, Ankita and Meher, N. K., "Arithmetic density and new congruences for 3 -core partitions" (2023). Journal Articles. 3473.
https://digitalcommons.isical.ac.in/journal-articles/3473