Extending Recent Congruence Results on (ℓ,μ)-Regular Overpartitions

2025/05/28 by Paudel, Bishnu, Sellers, James A., Wang, Haiyang
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.21989

Abstract

Recently, Alanazi, Munagi, and Saikia employed the theory of modular forms to investigate the arithmetic properties of the function R_ℓ,μ(n), which enumerates the overpartitions of n where no part is divisible by either ℓ or μ, for various integer pairs (ℓ, μ). In this paper, we substantially extend several of their results and establish infinitely many families of new congruences. Our proofs are entirely elementary, relying solely on classical q-series manipulations and dissection formulas.

Citations

• Further results on arithmetic properties of biregular overpartitions
• Arithmetic Properties of Generalized Cubic and Overcubic Partitions
• Some Properties of Overpartitions into Nonmultiples of Two Integers
• Ramanujan-type Congruences for Overpartitions Modulo 16

Related

• New arithmetic properties for overpartitions where nonoverlined parts are ℓ-regular
• Elementary Proofs of Recent Congruences for Overpartitions Wherein Non-Overlined Parts are Not Divisible by 6
• Some New Congruences For Overpartition Function With ℓ-Regular Non-Overlined Parts
• Some Properties of Overpartitions into Nonmultiples of Two Integers
• Arithmetic properties of overpartitions