Derivative polynomials and enumeration of permutations by number of interior and left peaks
Derivative polynomials and enumeration of permutations by number of interior and left peaks
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DOI：
10.1016/j.disc.2011.10.003
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Shi-Mei Ma
中科院分区：
文献类型：
--
作者：
Shi-Mei Ma
二元导数多项式是由正切函数和割线函数的重复微分定义的。我们建立了这些导数多项式的系数与对称群上的内峰和左峰的个数之间的联系。研究了对称群上内峰和左峰个数的母函数的性质，包括递归关系、母函数和实根性。
Derivative polynomials in two variables are defined by repeated differentiation of the tangent and secant functions. We establish the connections between the coefficients of these derivative polynomials and the number of interior and left peaks over the symmetric group. Properties of the generating functions for the number of interior and left peaks over the symmetric group, including recurrence relations, generating functions and real-rootedness, are studied.