December 2022 A formula on Stirling numbers of the second kind and its application to the unstable K-theory of stunted complex projective spaces
Osamu Nishimura
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Kyoto J. Math. 62(4): 763-788 (December 2022). DOI: 10.1215/21562261-2022-0026

Abstract

A formula on Stirling numbers of the second kind S(n,k) is proved. As a corollary, for odd n and even k, it is shown that k!S(n,k) is a positive multiple of the greatest common divisor of j!S(n,j) for k+1jn. Also, as an application to algebraic topology, some isomorphisms of unstable K1-groups of stunted complex projective spaces are deduced.

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Osamu Nishimura. "A formula on Stirling numbers of the second kind and its application to the unstable K-theory of stunted complex projective spaces." Kyoto J. Math. 62 (4) 763 - 788, December 2022. https://doi.org/10.1215/21562261-2022-0026

Information

Received: 10 July 2019; Revised: 17 July 2020; Accepted: 15 October 2020; Published: December 2022
First available in Project Euclid: 24 August 2022

MathSciNet: MR4518005
zbMATH: 1506.11037
Digital Object Identifier: 10.1215/21562261-2022-0026

Subjects:
Primary: 11B73
Secondary: 05A10 , 05A19 , 11B68 , 19L10 , 55N15

Keywords: Bernoulli numbers , complex James numbers , Stirling numbers of the second kind , stunted complex projective spaces , unstable K-theory

Rights: Copyright © 2022 by Kyoto University

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Vol.62 • No. 4 • December 2022
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