Singmaster-type results for Stirling numbers and some related diophantine equations

2023/11/10 by András Bazsó, Bazsó, András, István Mező +4
Mathematics · Physics and Astronomy · #11B73 #11D41 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.06080

openalex publication_date 2023/11/10 · openalex created_date 2023/11/14 · openalex updated_date 2026/07/28

Abstract

Motivated by the work of David Singmaster, we study the number of times an integer can appear among the Stirling numbers of both kinds. We provide an upper bound for the occurrences of all the positive integers, and present certain questions for further study. Some numerical results and conjectures concerning the related diohantine equations are collected.

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• Divisibility by 2 and 3 of certain Stirling numbers
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