论文标题
楼梯后粒细胞多项式
Staircase palindromic polynomials
论文作者
论文摘要
我们研究了一类一阶 - 上粒细胞多项式，我们称为楼梯palindromic多项式。具体而言，假设$ s（x，n，h）$是n的多项式，特殊形式：$ s（x; n; h）= x^n + 2x^{n-1} + 3x^{n-2} + \ dots + \ dots +（h-1） 1）X^{H-2} + \ DOTS + 2x + 1 $。然后，$ s（x，n，h）$可以考虑到环体多项式的产物。此外，对于任何给定的n，都有$ \ lceil {\ frac {n+1} {2} \ rceil} $阶梯式多项式，所有这些因素都可以借助环形多项式借助两个参数n和h得出。之后，我们探索一些可以转换为楼梯多项式的多项式类别。
We study a class of monic-palindromic polynomials that we call staircase palindromic polynomials. Specifically, suppose $S(x, n, h)$ is a polynomial of degree n with the special form: $S(x; n; h) = x^n + 2x^{n-1} + 3x^{n-2} + \dots + (h - 1)x^{n-h+2} + hx^{n-h+1} + \dots + hx^{h-1} + (h - 1)x^{h-2} + \dots + 2x + 1$. Then $S(x, n, h)$ can be factored as a product of cyclotomic polynomials. Moreover, for any given n, there are $ \lceil{\frac{n+1}{2}\rceil}$ staircase polynomials, all of whose factors can be derived using two parameter n and h with the help of cyclotomic polynomials. After that we explore some classes of polynomials that can be converted to staircase polynomials.
