Elementary Proofs of Recent Congruences for Overpartitions Wherein Non-Overlined Parts are Not Divisible by 6

2025/08/05 by Paudel, Bishnu, Sellers, James A., Wang, Haiyang
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.03927

Abstract

We define R_l^*(n) as the number of overpartitions of n in which non-overlined parts are not divisible by l. In a recent work, Nath, Saikia, and the second author established several families of congruences for R_l^*(n), with particular focus on the cases l=6 and l=8. In the concluding remarks of their paper, they conjectured that R₆^*(n) satisfies an infinite family of congruences modulo 128. In this paper, we confirm their conjectures using elementary methods. Additionally, we provide elementary proofs of two congruences for R₆^*(n) previously proven via the machinery of modular forms by Alanazi, Munagi, and Saikia.

Citations

• Some New Congruences For Overpartition Function With ℓ-Regular Non-Overlined Parts
• New arithmetic properties for overpartitions where nonoverlined parts are ℓ-regular
• Some Properties of Overpartitions into Nonmultiples of Two Integers

Related

• Extending Recent Congruence Results on (ℓ,μ)-Regular Overpartitions
• On Some New Congruences For Biregular Overpartitions
• Extending Congruences for the number of smallest parts in overpartitions with smallest part even
• New arithmetic properties for overpartitions where nonoverlined parts are ℓ-regular
• Some New Congruences For Overpartition Function With ℓ-Regular Non-Overlined Parts