Arithmetic properties of k-tuple ℓ-regular partitions

2024/12/16 by Hemjyoti Nath, Nath, Hemjyoti, Manjil P. Saikia +3
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2412.16193

Abstract

In this paper, we study arithmetic properties satisfied by the k-tuple ℓ-regular partitions. A k-tuple of partitions (ξ₁, ξ₂, …, ξ_k) is said to be ℓ-regular if all the ξ_i's are ℓ-regular. We study the cases (ℓ, k)=(2,3), (4,3), (ℓ, p), where p is a prime, and even the general case when both ℓ and k are unrestricted. Using elementary means as well as the theory of modular forms we prove several infinite family of congruences and density results for these family of partitions.

Related

• Extending recent work of Nath, Saikia, and Sarma on k-tuple ℓ-regular partitions
• Some congruences for (ℓ, k) and (ℓ, k, r)-regular partitions
• Arithmetic properties of the ℓ-regular partitions
• New arithmetic properties for overpartitions where nonoverlined parts are ℓ-regular
• Arithmetic properties of 5-regular partitions into distinct parts