2 citations · 2 across the 3 of their papers we have counts for
3 papers
math.NT2025
An infinite family of overpartition congruences mod powers of 2
Zhumagali Shomanov, Frank Garvan
We prove an infinite family of Hecke-like congruences for the overpartition function modulo powers of 2. Starting from a recent identity of Garvan and Morrow and iterating Atkin's…
math.NT2025
A simple proof of the Atkin-O'Brien partition congruence conjecture for powers of 13
Frank Garvan, Zhumagali Shomanov
In 1967, Atkin and O'Brien conjectured congruences for the partition function involving Hecke operators modulo powers of 13. In this paper, we provide a simple proof of this conjec…
math.CO2015★ 2 cited
Combinatorial Formula for the Partition Function
Zhumagali Shomanov
In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomi…