Some New Congruences for ℓ-Regular Multipartitions

2023/11/06 by Srilakshmi Krishnamoorthy, Krishnamoorthy, Srilakshmi, Abinash Sarma +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.03248

openalex publication_date 2023/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a positive integer n, let B_{ℓ1,…,ℓr}(n) denote the number of (ℓ₁,ℓ₂,⋯,ℓ_r)-regular multipartitions of n. If ℓ₁=ℓ₂=⋯=ℓ_r=ℓ, then we denote B_{ℓ1,…,ℓr}(n) as B_ℓ^(r)(n). In this paper, we prove several infinite families of congruences satisfied by B_ℓ^(r)(n) for different values of ℓ and r.

Related

• Extending Recent Congruence Results on (ℓ,μ)-Regular Overpartitions
• Some congruences for (ℓ, k) and (ℓ, k, r)-regular partitions
• Arithmetic density and congruences of ℓ-regular bipartitions II
• Arithmetic density and congruences of ℓ-regular bipartitions
• Some New Congruences For Overpartition Function With ℓ-Regular Non-Overlined Parts