Emergent Mind
Type-B analogue of Bell numbers using Rota's Umbral calculus approach
(2406.16393)
Published Jun 24, 2024
in
cs.DM
and
math.CO
Abstract
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.
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