On the arithmetic properties of partitions into parts simultaneously 4-regular and 9-distinct

2025/06/09 by Mohammed L. Nadji, Nadji, Mohammed L., Moussa Ahmia +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2506.07704

Abstract

In 2017, Keith presented a comprehensive survey on integer partitions into parts that are simultaneously regular, distinct, and/or flat. Recently, the authors initiated a study of partitions into parts that are simultaneously regular and distinct, examining them from both arithmetic and combinatorial perspectives. In particular, several Ramanujan-like congruences were obtained for \myRD^{(ℓ, t)}(n), the number of partitions of n into parts that are simultaneously ℓ-regular and t-distinct (parts appearing fewer than t times), for various pairs (ℓ, t). In this paper, we focus on the case (ℓ, t)=(4,9) and conduct a thorough investigation of the arithmetic properties of \myRD^{(4, 9)}(n). We establish several infinite families of congruences modulo 4, 6, and 12, along with a collection of Ramanujan-like congruences modulo 24.

Citations

• Arithmetic properties of t-Schur overpartitions
• Some Properties of Overpartitions into Nonmultiples of Two Integers
• A bijection for partitions simultaneously s-regular and t-distinct
• Multiplicative properties of the number of k-regular partitions
• Congruences for 9-regular partitions modulo 3

Cited by

• Extending Recent Congruence Results on t-Schur overpartitions

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