Multivariable Tangent and Secant q-derivative Polynomials
主 题: Multivariable Tangent and Secant q-derivative Polynomials
报告人: Prof. Guoniu Han (Université Louis Pasteur et C.N.R.S.)
时 间: 2013-12-06 10：00-11:00
地 点: 理科一号楼1493（主持人：宋春伟）
The derivative polynomials introduced by Knuth and Buckholtz in their calculations of the tangent and secant numbers are extended to a multivariable q-environment. The n-th q-derivatives of the classical q-tangent and q-secant are given two polynomial expressions in q-tangent and q-secant, indexed by triplets of integers for the first class, and compositions of integers for the second. The functional relation between those two classes is fully given by means of combinatorial techniques. Moreover, those polynomials are proved to be generating functions for so-called t-permutations by multivariable statistics. By giving special values to those polynomials we recover classical q-polynomials such as the Carlitz q-Eulerian polynomials and the (t,q)-tangent and -secant analogs recently introduced
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