The minimal odd excludant and Euler’s partition theorem

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-03-26 DOI:10.1142/s1793042124500714

Andrew Y. Z. Wang, Zheng Xu

引用次数: 0

Abstract

In this work, we establish two interesting partition identities involving the minimal odd excludant, which has attracted great attention in recent years. In particular, we find a strong refinement of Euler’s celebrated theorem that the number of partitions of an integer into odd parts equals the number of partitions of that integer into distinct parts.

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最小奇数不等式和欧拉分割定理

在这项工作中，我们建立了两个涉及最小奇数不等式的有趣的分割等式，该等式近年来引起了极大的关注。特别是，我们发现了欧拉著名定理的有力改进，即把一个整数分割成奇数部分的个数等于把该整数分割成不同部分的个数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.