Rota used the functional L to recover old properties and obtain some new formulas for the Bell numbers. Tanny used Rota's functional L and the celebrated Worpitzky identity to obtain some expression for the ordered Bell numbers, which can be seen as an evident to the fact that the ordered Bell numbers are gamma-positive. In this paper, we extend some of Rota's and Tanny's results to the framework of the set partitions of Coxeter type B.

翻译：罗塔利用泛函L恢复了贝尔数的经典性质并推导出若干新公式。坦尼运用罗塔泛函L与著名的沃皮茨基恒等式，得到了有序贝尔数的若干表达式，这为有序贝尔数具有伽马正性提供了明确证据。本文将在考克斯特B型集合划分的框架下，推广罗塔与坦尼的部分研究成果。