截断二项式展开式的一些不可约结果
Some irreducibility results for truncated binomial expansions
摘要：
对于正整数$n>k$，令$P_{n,k}(x)=\displaystyle\sum_{j=0}^k \binom{n}{j}x^j $为通过在$k^{th}$阶段截断$(1+x)^n$的二项式展开而获得的多项式。这些多项式出现在调查舒伯特演算在格拉斯曼。本文证明了当$P_{n,k}(x)$.
英文摘要：
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 $2\leqslant 2k \leqslant n<(k+1)^3$.
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