Congruences for 5-Regular Partitions with Odd Parts Overlined

Abstract

Let a₅(n) denote the number of 5-regular partitions of n with the first occurrence of an odd number may be overlined. In this paper, we establish many infinite families of congruences modulo powers of 2 for a₅(n). For example, for all
n ≥ 0 and β ≥ 0,
a₅ (16 · 5^2β+1n +k₁ · 5^2β − 1/3 ) ≡ 0 (mod 16),
where k₁ ∈ {142, 238}.

Key words and phrases. Congruences, regular partitions, over partitions.

2010 Mathematics Subject Classification. 11P83; 05A17