A direct approach to the Gallai-Schur numbers

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This is a Quantitative Study study.

Fred Rowley

doi:10.48550/arxiv.2503.02136

March 3, 2025Open Access

A direct approach to the Gallai-Schur numbers

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Key Points

Maximal weak and strong Gallai-Schur partitions are characterized, providing a new understanding of these structures.
The findings confirm values of Gallai-Schur numbers determined by Budden in 2020, enhancing previous work.
Elementary proofs support the structure of Gallai-Schur partitions, making the results accessible and standalone.
Exact values for weak Gallai-Schur numbers are also established, extending the application of Gallai-Schur theory.

Implication

The paper reveals exact values of Gallai-Schur numbers in strong and weak cases, implying significant structural insights.

Abstract

This paper characterises the structure of every maximal weak or strong Gallai-Schur partition. The results confirm the exact values of Gallai-Schur numbers provided by Budden (2020) in the strong case, and provide corresponding values for weak Gallai-Schur numbers. The proofs are elementary and standalone.

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Cite This Study

Fred Rowley (2025) studied this question.

synapsesocial.com/papers/68f64fbb2509bc8625bfb170 https://doi.org/10.48550/arxiv.2503.02136

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A direct approach to the Gallai-Schur numbers

Key Points

Implication

Abstract

Discussion

Cite This Study

A direct approach to the Gallai-Schur numbers

Key Points

Implication

Abstract

Discussion

Cite This Study

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