On the irreducibility of a truncated binomial expansion

Michael Filaseta, Angel Kumchev, Dmitrii V. Pasechnik

Published 2004-09-27, updated 2004-12-04Version 2

Let P_nk(x) denote the sum of the lowest k+1 terms in the expansion of (1+x)^n. We investigate the irreducibility of P_nk(x) and more general univariate polynomials related to it. Polynomials P_nk(x) naturally arise in Schubert calculus, see ArXiv e-print math.RT/0409329 by I.Scherbak.