Some Properties of Overpartitions into Nonmultiples of Two Integers

2024/12/25 by Alanazi, Abdulaziz M., Munagi, Augustine O., Saikia, Manjil P. · 7 citations
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.18938

Abstract

We consider properties of overpartitions that are simultaneously ℓ-regular and μ-regular, where ℓ and μ are positive relatively prime integers. We prove a seven-way combinatorial identity related to these overpartitions. We also prove several congruence properties satisfied by this class of partitions (and a further related class) using both generating functions and modular forms with Radu's Algorithm.

Cited by

• Arithmetic properties of t-Schur overpartitions
• Extending Recent Congruence Results on t-Schur overpartitions
• Elementary Proofs of Recent Congruences for Overpartitions Wherein Non-Overlined Parts are Not Divisible by 6
• On Some New Congruences For Biregular Overpartitions
• Some new congruences on biregular overpartitions
• On the arithmetic properties of partitions into parts simultaneously 4-regular and 9-distinct
• Extending Recent Congruence Results on (ℓ,μ)-Regular Overpartitions

Related

• Extending Recent Congruence Results on (ℓ,μ)-Regular Overpartitions
• New arithmetic properties for overpartitions where nonoverlined parts are ℓ-regular
• Arithmetic properties of overpartitions
• Separable integer partition classes and partitions with congruence conditions
• Some New Congruences For Overpartition Function With ℓ-Regular Non-Overlined Parts