论文标题
某些指数sheffer序列的零基因座和某些组合特性
The zero locus and some combinatorial properties of certain exponential Sheffer sequences
论文作者
论文摘要
我们介绍了有关Sheffer序列的组合和分析结果，该序列具有$ g（s，z）= e^{czs+αz^{2}+βZ^{4}} $的指数生成函数，其中$α，β，β，c \ in \ in \ nne \ nne $ c {我们证明，在这种sheffer序列中，所有多项式的零是真实的，要么纯粹是虚构的。此外，使用Riordan矩阵的特性，我们表明我们的Sheffer序列满足了阶4的三个复发关系，并且我们还表现出这些Sheffer多项式的系数与某些标记的生成树中给定标记的节点的系数与A给定标签的数量之间的联系。
We present combinatorial and analytical results concerning a Sheffer sequence with an exponential generating function of the form $G(s,z)=e^{czs+αz^{2}+βz^{4}}$, where $α, β, c \in \mathbb{R}$ with $β<0$ and $c\neq 0$. We demonstrate that the zeros of all polynomials in such a Sheffer sequence are either real, or purely imaginary. Additionally, using the properties of Riordan matrices we show that our Sheffer sequence satisfies a three-term recurrence relation of order 4, and we also exhibit a connection between the coefficients of these Sheffer polynomials and the number of nodes with a a given label in certain marked generating trees.
