On the biases and asymptotics of partitions with finite choices of parts

2024/04/06 by Jiyou Li, Sicheng Zhao, Li, Jiyou +1
Mathematics · #05A17 11P81 #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.04588

openalex publication_date 2024/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Biases in integer partitions have been studied recently. For three disjoint subsets R,S,I of positive integers, let p_RSI(n) be the number of partitions of n with parts from R∪ S∪ I and p_R>S,I(n) be the number of such partitions with more parts from R than that from S. In this paper, in the case that R,S,I are finite we obtain a concrete formula of the asymptotic ratio of p_R>S,I(n) to p_RSI(n). We also propose a conjecture in the case that R,S are certain infinite arithmetic progressions.

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