INEQUALITIES FOR THE CUBIC PARTITIONS AND CUBIC PARTITION PAIRS

doi:10.1007/s10473-025-0225-4

Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 737-754.doi: 10.1007/s10473-025-0225-4

INEQUALITIES FOR THE CUBIC PARTITIONS AND CUBIC PARTITION PAIRS

Chong Li¹, Yi Peng¹, Helen W.J. Zhang^1,2,*

1. School of Mathematics, Hunan University, Changsha 410082, China;
2. Research Institute of Hunan University in Chongqing, Chongqing 401120, China

Received:2023-12-30 Online:2025-03-25 Published:2025-05-08
Contact: *Helen W.J. Zhang, E-mail: helenzhang@hnu.edu.cn
About author:Chong Li, E-mail: chongli@hnu.edu.cn;Yi Peng, E-mail: iampenny@hnu.edu.cn
Supported by:
This research was supported by the National Natural Science Foundation of China (12371327) and the Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0107).

Abstract

Abstract: In this paper, we examine the functions $a(n)$ and $b(n)$ , which respectively represent the number of cubic partitions and cubic partition pairs. Our work leads to the derivation of asymptotic formulas for both $a(n)$ and $b(n)$ . Additionally, we establish the upper and lower bounds of these functions, factoring in the explicit error terms involved. Crucially, our findings reveal that $a(n)$ and $b(n)$ both satisfy several inequalities such as log-concavity, third-order Turán inequalities, and strict log-subadditivity.

Key words: asymptotic formula, log-concavity, third-order Turán inequalities, cubic partition, cubic partition pair

CLC Number:

05A20

Chong Li, Yi Peng, Helen W.J. Zhang. INEQUALITIES FOR THE CUBIC PARTITIONS AND CUBIC PARTITION PAIRS[J].Acta mathematica scientia,Series B, 2025, 45(2): 737-754.

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INEQUALITIES FOR THE CUBIC PARTITIONS AND CUBIC PARTITION PAIRS

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