Integer Partitions With Restricted Distinct Parts

2025/08/18 by Drema, Rinchin, Saikia, Nipen
#05A15 #05A17 #11P83 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.12739

Abstract

For any positive integers s and t, let Q_t^s(n) denotes the number of partitions of a positive integer n into distinct parts such that no part is congruent to s or t-s modulo t. We prove some Ramanujan-type congruences for Q_t^s(n) for some particular values of s and t by employing q-series and theta function identities.

Related

• Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function
• Some New Congruences for l-Regular Partitions Modulo l
• Two partition functions with congruences modulo 3, 5, 7, and 13
• Congruences for an analogue of Lin's partition function
• On the arithmetic properties of partitions into parts simultaneously 4-regular and 9-distinct