Theta-type congruences for colored partitions

2022/06/23 by Olivia Beckwith, Beckwith, Olivia, Alexander Caione +8 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2206.11779

openalex publication_date 2022/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate congruence relations of the form p_r(ℓ m n + t) ≡ 0 \pmodℓ for all n, where p_r(n) is the number of r-colored partitions of n and m,ℓ are distinct primes.

Cited by

• Rademacher-type exact formula and higher order Turán inequalities for r-colored ℓ-regular partitions

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• Congruence relations for r-colored partitions
• Arithmetic properties of (ℓ,m)-regular colored partitions
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• General Congruences Modulo 5 and 7 for Colour Partitions
• Congruences for generalized Color Partitions of Hirschhorn and Sellers