Congruences for 9-regular partitions modulo 3

2013/06/01 by William J. Keith, Keith, William J. · 1 citation
Mathematics · #05A17 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1306.0136

openalex publication_date 2013/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that the number of 9-regular partitions of n is divisible by 3 when n is congruent to 3 mod 4, and by 6 when n is congruent to 13 mod 16. An infinite family of congruences mod 3 holds in other progressions modulo powers of 4 and 5. A collection of conjectures includes two congruences modulo higher powers of 2 and a large family of "congruences with exceptions" for these and other regular partitions mod 3.

Cited by

• On the arithmetic properties of partitions into parts simultaneously 4-regular and 9-distinct

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