Arithmetic properties of k-tuple ℓ-regular partitions

Abstract

In this paper, we study arithmetic properties satisfied by the k-tuple ℓ-regular partitions. A k-tuple of partitions (ξ1,ξ2,…,ξk) is said to be ℓ-regular if all the ξi'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 this family of partitions. © 2025 Elsevier Inc.