Theoretical Statistics and Mathematics Unit, ISI Delhi

Some irreducibility results for truncated binomial expansions

by Sudesh K. Khanduja, Ramneek Khassa and Shanta Laishram

For positive integers $n>k$, let $P_{n,k}(x)=\displaystyle\sum_{j=0}^k \binom{n}{j}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\leqslant 2k \leqslant n<(k+1)^3 $.

isid/ms/2011/07 [fulltext]

Click here to return to Preprints Page