Treffer: A formula on Stirling numbers of the second kind and its application to the unstable K-theory of stunted complex projective spaces: A formula on Stirling numbers of the second kind and its application to the unstable \(K\)-theory of stunted complex projective spaces
Title:
A formula on Stirling numbers of the second kind and its application to the unstable K-theory of stunted complex projective spaces: A formula on Stirling numbers of the second kind and its application to the unstable \(K\)-theory of stunted complex projective spaces
Authors:
Source:
Kyoto Journal of Mathematics. 62
Publication Status:
Preprint
Publisher Information:
Duke University Press, 2022.
Publication Year:
2022
Subject Terms:
Mathematics - Number Theory, 05A10, 05A19, 11B68, 11B73, 19L10, 55N15, Bell and Stirling numbers, 01 natural sciences, Stirling numbers of the second kind, Riemann-Roch theorems, Chern characters, stunted complex projective spaces, Topological \(K\)-theory, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), complex James numbers, Mathematics - Algebraic Topology, Combinatorics (math.CO), Number Theory (math.NT), 0101 mathematics, Bernoulli and Euler numbers and polynomials, Bernoulli numbers, unstable \(K\)-theory
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
ISSN:
2156-2261
DOI:
10.1215/21562261-2022-0026
DOI:
10.48550/arxiv.1906.00384
Access URL:
Rights:
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....8ed362b85e266f827f2050861482a66f
Database:
OpenAIRE
Weitere Informationen
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 $k+1\leq j\leq n$. Also, as an application to algebraic topology, some isomorphisms of unstable $K^1$-groups of stunted complex projective spaces are deduced.
27 pages