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A Local Limit Theorem for Integer Partitions into Small Powers

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arxiv 2311.09203 v1 pith:CBB4BF6Y submitted 2023-11-15 math.CO math.NT

Gabriel F. Lipnik , Manfred G. Madritsch , Robert F. Tichy This is my paper · ORCID
classification math.COmath.NT
keywords partitionslimitlocalpowerstheoremalphacombinatoricsconsiderations
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abstract

The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers $0<\alpha<1$ were of recent interest. In the present paper we want to extend our considerations of the length of a random partition by providing a local limit theorem.

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  1. Proof of a conjecture by Starr and log-concavity for random commuting permutations

    math.CO 2025-06 conditional novelty 8.0 of 10

    The paper proves Starr's conjecture on the asymptotics of A(ℓ,n,k), the number of commuting ℓ-tuples of permutations with k joint orbits, and derives log-concavity for typical k.

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