关于第二类Stirling数的一个公式及其在发育复射影空间的不稳定K理论中的应用

IF 0.5 4区数学 Q3 MATHEMATICS

Kyoto Journal of Mathematics Pub Date : 2019-06-02 DOI:10.1215/21562261-2022-0026

O. Nishimura

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引用次数: 0

摘要

证明了第二类斯特林数的一个公式$S(n, k)$。作为推论，对于奇数$n$和偶数$k$，表明$k!S(n, k)$是$k+1\leq j\leq n$的最大公约数$j!S(n, j)$的正倍数。同时，作为代数拓扑的应用，导出了发育不良复射影空间中不稳定$K^1$ -群的一些同构。

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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 $S(n, k)$ 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.

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来源期刊

Kyoto Journal of Mathematics MATHEMATICS-

CiteScore

1.10

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyoto Journal of Mathematics publishes original research papers at the forefront of pure mathematics, including surveys that contribute to advances in pure mathematics.