Sep 28, 2004 · The two functions are related by the following formula:(4) r k ( n ) = 2 k c k ( n ) + ∑ i = 1 k k i ( - 1 ) i - 1 r k - i ( n ) , which is the ...

The two functions are related by the following formula: (4) rk(n)=2kck(n) + k. X i=1 ki (−1)i−1rk−i(n),. Page 3. THE OVERPARTITION FUNCTION MODULO SMALL POWERS ...

In this article, we establish several infinite families of Ramanujan-type congruences modulo 16, 32 and 64 for po(n), the number of overpartitions of n in which ...

Oct 22, 2024 · In fact Mahlburg [10] conjectured that the overpartition function is almost always divisible by arbitrary powers of 2, which is still open. The ...

In a recent paper, Fortin et al. (Jagged Partitions, arXivmath. CO/0310079, 2003) found congruences modulo powers of 2 for the values of the overpartition ...

Dec 19, 2023 · In this paper we prove several Ramanujan-type congruences modulo powers of 2 2 2 2 for the functions O ⁢ P ⁢ T ¯ 2 ⁢ k + 1 ⁢ ( n ) subscript ¯ 𝑂 ...

An overpartition of n is a non-increasing sequence of positive integers whose sum is n in which the first occurrence of a number may be overlined.

Dec 14, 2023 · The objective of this paper is to establish some new internal congruences and con- gruences modulo powers of 2 for overpartition function and ...

Mahlburg, K.: The overpartition function modulo small powers of $$2$$ 2 . Discret. Math. 286, 263–267 (2004) https://doi.org/10.1016/j.disc.2004.03.014 ...

Feb 15, 2019 · We find congruences modulo 32, 64 and 128 for the partition function ppo(n), the number of overpartition pairs of n into odd parts, with the aid ...