Some irreducibility results for truncated binomial expansions

Abstract

For positive integers $n>k$, let $P_{n,k}(x)=\sum _{j=0}^k\left(\genfrac{}{}{0ex}{}{n}{j}\right)x^j$ be the polynomial obtained by truncating the binomial expansion of $(1+x{)}^n$ at the $k^{th}$ stage. These polynomials arose in the investigation of Schubert calculus in Grassmannians. In this paper, the authors prove the irreducibility of $P_{n,k}(x)$ over the field of rational numbers when $2⩽2k⩽n<(k+1{)}^3$.

References in corpus (1)

• Intersections of Schubert varieties and highest weight vectors in tensor products of sl_{N+1}-representations

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