INFINITE FAMILIES OF CONGRUENCES MODULO 2 FOR 2-CORE AND 13-CORE PARTITIONS

Article Type

Research Article

Publication Title

Journal of the Korean Mathematical Society

Abstract

A partition of n is called a t-core partition if none of its hook number is divisible by t. In 2019, Hirschhorn and Sellers [5] obtained a parity result for 3-core partition function a3(n). Motivated by this result, both the authors [8] recently proved that for a non-negative integer α, aα3m(n) is almost always divisible by an arbitrary power of 2 and 3 and at(n) is almost always divisible by an arbitrary power of pji, where j is a fixed positive integer and t = pa1 1pa2 2· · · pamm with primes pi ≥ 5. In this article, by using Hecke eigenform theory, we obtain infinite families of congruences and multiplicative identities for a2(n) and a13(n) modulo 2 which generalizes some results of Das [2].

First Page

1073

Last Page

1085

DOI

https://10.4134/JKMS.j230031

Publication Date

9-1-2023

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