广义Stirling数的单峰型性质

Unimodality properties of generalized Stirling numbers

本文研究由徐利治和薛昭雄引进的广义Stirling数相关的一些单峰型问题,主要结果包括某些广义Bell数的对数凸性、广义Bell多项式的实零点性、广义Bell多项式序列的q-对数凸性和广义Stirling数相应的线性变换的保对数凸性.

In this paper, we study various unimodality properties of generalized Stirling numbers introduced by Hsu and Shiue. We obtain the log-convexity of generalized Bell numbers, the reality of zeros and the q-log- convexity of generalized Bell polynomials. We also show that certain linear transformations associated with generalized Stirling numbers preserve the log-convexity.