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

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Inequalities for the cubic partitions and cubic partition pairs

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Chong Li,
  • Yi Peng,
  • Helen W. J. Zhang

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 Turán inequalities, and strict log-subadditivity.