A formula on Stirling numbers of the second kind and its application to the unstable K-theory of stunted complex projective spaces

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+1≤j≤n. Also, as an application to algebraic topology, some isomorphisms of unstable K1-groups of stunted complex projective spaces are deduced.