2024/06/28 by Thomas Y. He, He, Thomas Y., C. S. Huang +5 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2406.19823
openalex publication_date 2024/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we first investigate the partitions whose parts are congruent to a or b modulo k with the aid of separable integer partition classes with modulus k introduced by Andrews. Then, we introduce the (k,r)-overpartitions in which only parts equivalent to r modulo k may be overlined and we will show that the number of (k,k)-overpartitions of n equals the number of partitions of n such that the k-th occurrence of a part may be overlined. Finally, we extend separable integer partition classes with modulus k to overpartitions and then give the generating function for (k,r)-modulo overpartitions, which are the (k,r)-overpartitions satisfying certain congruence conditions.