论文标题
交替运行排列和中央阶乘数字
Alternating runs of permutations and the central factorial numbers
论文作者
论文摘要
令r（n，k）为$ \ {1,2，\ ldots，n \} $的置换次数，然后使用k交替运行。在本文中，我们建立了r（n，k）与均匀索引的中央阶乘数量以及具有给定数量的交替运行数量的签名排列数量与奇数索引的中央阶乘数量之间的关系。还建立了峰值和左峰多项式的显式公式，用于置换和切线和割线函数的导数多项式。
Let R(n,k) be the number of permutations of $\{1,2,\ldots,n\}$ with k alternating runs. In this paper, we establish the relationships between R(n,k) and the central factorial numbers of even indices as well as the number of signed permutations with a given number of alternating runs and the central factorial numbers of odd indices. The explicit formulas of the peak and left peak polynomials for permutations and the derivative polynomials of the tangent and secant functions are also established.
