On 2-color partitions where one of the colors is multiples of 7^k

2025/04/02 by Gireesh, D. S., C., Shivashankar, B, HemanthKumar
#05A17 #FOS: Mathematics #Number Theory (math.NT) #primary 11P83 #secondary 05A15

paper · doi:10.48550/arxiv.2504.01518

Abstract

In this work, we investigate the arithmetic properties of p_1,7^k(n), which counts 2-color partitions of n where one of the colors appears only in parts that are multiples of 7^k. By constructing generating functions for p_1,7^k(n) across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of 7.

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