Ramanujan-Type congruences for cubic partition functions

2010/03/01 by Xinhua Xiong, Xiong, Xinhua
Mathematics · #11p83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1003.0241

openalex publication_date 2010/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The cubic partitions of a natural number n, introduced by Chan and Kim, have generating function ∑_n=0^∞a(n)qⁿ= \frac1(q; q)_∞(q²; q²)_∞. In this paper, we generalize some results of Chen-Lin, which suggest that a(n) should have analogous properties of the ordinary partition function. Specifically, we show that for every non-negative integer n, a(5⁴n+547)≡ 0\pmod5², a(7³n+190)≡ 0\pmod7², a(7³n+288 ≡ 0\pmod7² and a(7³n+337)≡ 0\pmod7².

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