INEQUALITIES FOR THE CUBIC PARTITIONS AND CUBIC PARTITION PAIRS  

作　　者：Chong LI Yi PENG Helen W.J.ZHANG 李冲;彭祎;张文静

机构地区：[1]School of Mathematics,Hunan University,Changsha 410082,China [2]Research Institute of Hunan University in Chongqing,Chongqing 401120,China

出　　处：《Acta Mathematica Scientia》2025年第2期737-754,共18页数学物理学报(B辑英文版)

基　　金：supported by the National Natural Science Foundation of China(12371327);the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0107).

摘　　要：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 Turan inequalities,and strict log-subadditivity.

关 键 词：asymptotic formula LOG-CONCAVITY third-order Turan inequalities cubic partition cubic partition pair 

分 类 号：O156[理学—数学]