February 21, 2024

The minimal odd excludant and Euler’s partition theorem

Key Points

Findings reveal strong refinements of classic partition identities, enhancing understanding of partitions.
The established partition identities relate partitions into odd parts and distinct parts through the minimal odd excludant.
This analysis uses advanced mathematical techniques to explore the nature of partitions in number theory and combinatorics, revealing new insights.

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.

The minimal odd excludant and Euler’s partition theorem

Key Points

Abstract

Cite This Study