Arithmetic Identities and Congruences for Partition Triples with 3-cores

2015/02/23 by Liuquan Wang, Wang, Liuquan
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 05A17 #Secondary 11P83 #math.CO #math.NT #msc:05A17 #msc:11P83

paper · pdf · doi:10.48550/arxiv.1502.06454

14 pages

arxiv created 2015/02/23 · openalex publication_date 2015/02/23 · arxiv updated 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B₃(n) denote the number of partition triples of n where each partition is 3-core. With the help of generating function manipulations, we find several infinite families of arithmetic identities and congruences for B₃(n). Moreover, let ω(n) denote the number of representations of a nonnegative integer n in the form x₁²+x₂²+x₃²+3y₁²+3y₂²+3y₃² with x₁,x₂,x₃,y₁,y₂,y₃∈ ℤ. We find three arithmetic relations between B₃(n) and ω(n), such as ω(6n+5)=4B₃(6n+4).

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