Strict log-concavity of k -coloured partitions

Q: What does this research mean for the field?

The log-concavity of k-coloured partitions is strict for k ≥ 2, and the partition function respects the Hardy-Littlewood-Pólya majorization order. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Kathrin Bringmann; Ben Kane; Anubhab Pahari; Larry Rolen

doi:10.1017/prm.2026.10154

May 18, 2026Proceedings of the Royal Society of Edinburgh Section A MathematicsOpen Access

Strict log-concavity of k -coloured partitions

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Key Points

The aim is to prove that the log-concavity of k-coloured partitions is strict for k≥2.
Introduced recursive sequences and strict inequalities for fractional partition functions.
Utilized Hardy–Littlewood–Pólya’s majorizing concept to analyze partition functions.
Proved strict log-concavity for k-coloured partitions when k≥2.
Established explicit errors in fractional partition functions.

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Implication

This randomized trial demonstrates strict log-concavity of k-coloured partitions, suggesting new insights into partition functions.

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Cite This Study

Bringmann et al. (2026) studied this question.

synapsesocial.com/papers/6a0d50dcf03e14405aa9d02b https://doi.org/10.1017/prm.2026.10154

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Strict log-concavity of k -coloured partitions

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Strict log-concavity of k -coloured partitions

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Implication

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