arXiv 2403.095812024-03math.CO

Roman阶乘的通用定义：基础函数与泛化过程导论

Universal Definitions of the Roman Factorial: Introduction to Foundational Functions and the Generalization Process

Leonidas Liponis

备注：: 24 pages, 16 figures (v2: submission date now shows correctly) (v3: fixed typo, added contact email, added footnote to explain citations) (v4: various latex optimizations) (v5: fixed domain mislabeling in introduction) (v6: adjusted phrasing for clarity) (v7: minor latex modifications in preparation for the follow-up paper) (v8: further latex and formatting improvements)

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AI总结：

本文提出一组类似布尔运算的非闭式基础函数，并通过系统化泛化过程构建Roman阶乘的递归与非递归全局定义。

摘要：

本文介绍了一种利用非闭式表达的普适函数重新定义Roman阶乘的新方法。我们提出了一组类似于布尔运算的基础函数，以简化阶乘表达式。通过一个被称为“泛化过程”的系统化泛化流程，本文旨在利用这些基础函数创建Roman阶乘的递归与非递归全局定义。

英文摘要：

This paper introduces a new method for redefining the Roman factorial using universally applicable functions that are not expressed in closed form. We present a set of foundational functions, similar to Boolean operations, to simplify the factorial expression. Through a systematic process of generalization, termed generalization process, we aim to use these foundational functions to create recursive and non-recursive, global definitions of the Roman factorial.

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