论文标题
Riordan矩阵的分子多项式
Numerator polynomials of the Riordan matrices
论文作者
论文摘要
Riordan矩阵是与正式功率系列空间中某些操作员相对应的无限下三角矩阵。概括的Euler多项式$ {{g} _ {n}} \ left（x \ right）= {{{\ left（1-x \ oright）}^{n+1}} \ sum \ sum \ nolimits_ \ right）{{x}^{m}} $，其中$ {{p} _ {n}} \ left（m \ right）$是度$ \ le n $的多项式，是普通riordan Matrices对基因对基的生成函数的numerator polynomials。概括的narayana polyenmials $ {{h} _ {n}} \ left（x \ firt）= {{{\ left（1-x \ oright）}^{2n+1}} \ sum \ sum \ nolimits_ \ right）{{p} _ {n}}} \ left（m \ right）{{x}^{m}} $是指数riordan矩阵对角的生成函数的分子多项式。在纸上，考虑了这两种类型的分子多项式的特性及其之间的建设性关系。对与$ _ {\ left（β\右）} a \ left（x \ firt）= a \ left（x {} _ {\ left（β\ \右）} {a} {a} {a} {$左）{
Riordan matrices are infinite lower triangular matrices corresponding to the certain operators in the space of formal power series. Generalized Euler polynomials ${{g}_{n}}\left( x \right)={{\left( 1-x \right)}^{n+1}}\sum\nolimits_{m=0}^{\infty }{{{p}_{n}}}\left( m \right){{x}^{m}}$, where ${{p}_{n}}\left( m \right)$ is the polynomial of degree $\le n$, are the numerator polynomials of the generating functions of diagonals of the ordinary Riordan matrices. Generalized Narayana polynomials ${{h}_{n}}\left( x \right)={{\left( 1-x \right)}^{2n+1}}\sum\nolimits_{m=0}^{\infty }{\left( m+1 \right)...\left( m+n \right){{p}_{n}}}\left( m \right){{x}^{m}}$ are the numerator polynomials of the generating functions of diagonals of the exponential Riordan matrices. In paper, the properties of these two types of numerator polynomials and the constructive relationships between them are considered. Separate attention is paid to the numerator polynomials of Riordan matrices associated with the family of series $_{\left( β\right)}a\left( x \right)=a\left( x{}_{\left( β\right)}{{a}^{β}}\left( x \right) \right)$.
