What question did this study set out to answer?

The aim is to complete the classification of maximal unrefinable partitions and relate them to suitable partitions into distinct parts.

February 16, 2026Open Access

The number of maximal unrefinable partitions

Q: What does this research mean for the field?

The number of maximal unrefinable partitions of an integer coincides with the number of suitable partitions into distinct parts, depending on the distance from the successive triangular number. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Key Points

The aim is to complete the classification of maximal unrefinable partitions and relate them to suitable partitions into distinct parts.
Extended theoretical framework based on previous work by Aragona et al.
Analysis of the relationship between maximal unrefinable partitions and triangular numbers.
Examined distances from successive triangular numbers to determine partition types.
Identified that the number of maximal unrefinable partitions matches suitable partitions into distinct parts.
Demonstrated the dependency on the distance from successive triangular numbers.

Abstract

Abstract This paper completes the classification of maximal unrefinable partitions, extending a previous work of Aragona et al. devoted only to the case of triangular numbers. We show that the number of maximal unrefinable partitions of an integer coincides with the number of suitable partitions into distinct parts, depending on the distance from the successive triangular number.

Mark Helpful

Bookmark

Relay

View Full Paper