Asymptotics for k-crank of k-colored partitions

2023/04/13 by Helen W. J. Zhang, Ying Zhong, Zhang, Helen W. J. +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2304.06316

openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain asymptotic formulas for k-crank of k-colored partitions. Let M_k(a, c; n) denote the number of k-colored partitions of n with a k-crank congruent to a mod c. For the cases k=2,3,4, Fu and Tang derived several inequality relations for M_k(a, c; n) using generating functions. We employ the Hardy-Ramanujan Circle Method to extend the results of Fu and Tang. Furthermore, additional inequality relations for M_k(a, c; n) have been established, such as logarithmic concavity and logarithmic subadditivity.

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