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

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András Bazsó, István Mező, {Ákos Pintér, Szabolcs Tengely

Number Theory · Submitted 10 Nov 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We provide an upper bound for the occurrences of all the positive integers, and present certain questions for further study.

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arXiv ID2311.06080 (version 1)
Pith ID3RZD3SCY, Pith's permanent record of this paper and its review
Citation{\'A}kos Pint\'er, Andr\'as Bazs\'o, Istv\'an Mez\H{o}, Szabolcs Tengely. "Singmaster-type results for Stirling numbers and some related diophantine equations." arXiv:2311.06080 (2023). https://pith.science/paper/3RZD3SCY
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,877 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.48 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Motivated by the work of David Singmaster, we study the number of times an integer can appear among the Stirling numbers of both kinds. background 0.61 0.32 0.06 asserted 0.69
s1 We provide an upper bound for the occurrences of all the positive integers, and present certain questions for further study. result 0.54 0.95 0.69 asserted 1.00
s2 Some numerical results and conjectures concerning the related diohantine equations are collected. contribution 0.75 0.82 0.06 asserted 0.88

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

What was examined, and what was not

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not examined
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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