Arithmetic properties of (ℓ,m)-regular colored partitions

2025/05/18 by N., Yashas, Shivashankar, C., Chandankumar, S.
#05A15 #05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.12270

Abstract

Let b^k_ℓ,m(n) denotes the number of k-colored partitions of n into parts that are not multiples of ℓ or m. We establish several congruence relations for b_ℓ,m(n). For instance, for any nonnegative integer n b²_4,5(8n+7) ≡ 0 \pmod40.

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