发表机构
National Institute of Technology Calicut（印度国家技术学院卡利卡特分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究广义彩色超分拆函数 $\overline{\mathfrak{C}}_{m,r,s}(n)$，给出其渐近公式并探讨算术与密度性质。
AI 中文摘要
彩色分拆构成了一个成熟且被广泛研究的研究领域，通过对部分允许的颜色施加限制，产生了众多推广。特别是，受限彩色分拆因其丰富的组合与算术性质而受到相当大的关注。受这些发展的启发，我们考虑一个彩色超分拆函数 $\overline{\mathfrak{C}}_{m,r,s}(n)$，它枚举 $n$ 的超分拆，使得每个可被 $m$ 整除的部分可以被赋予 $r$ 种颜色中的任意一种，而每个不能被 $m$ 整除的部分可以被赋予 $s$ 种颜色中的任意一种。我们研究了该函数的渐近公式和若干算术性质，包括其密度性质。
英文摘要
Colored partitions constitute a well-established and extensively studied area of research with numerous generalizations arising from imposing restrictions on the allowed colors of the parts. In particular, restricted colored partitions have received considerable attention owing to their rich combinatorial and arithmetic properties. Motivated by these developments, we consider a colored overpartition function $\overline{\mathfrak{C}}_{m,r,s}(n)$, which enumerates the overpartitions of $n$ such that each part divisible by $m$ can be assigned any of $r$ colors, while each part not divisible by $m$ may be assigned any of $s$ colors. We investigate an asymptotic formula and several arithmetic properties of this function, including its density properties.
