A certain property of polynomials and the CI-stability of tangent bundle over projective spaces

Bull. Korean Math. Soc. 2007 Vol. 44, No. 1, 83-86 Printed March 1, 2007

Ryuichi Tanaka Tokyo University of Science

Abstract : We determine the largest integer $i$ such that $0< i \leq n$ and the coefficient of $t^i$ is odd in the polynomial $(1+t+t^2+\cdots +t^n)^{n+1}$. We apply this to prove that the co-index of the tangent bundle over ${FP}^n$ is stable if $2^r\leq n<2^r+\frac{1}{3}(2^r-2)$ for some integer $r$.