The deranged Bell numbers
General Mathematics
2021-02-02 v1
Abstract
It is known that the ordered Bell numbers count all the ordered partitions of the set . In this paper, we introduce the deranged Bell numbers that count the total number of deranged partitions of . We first study the classical properties of these numbers (generating function, explicit formula, convolutions, etc.), we then present an asymptotic behavior of the deranged Bell numbers. Finally, we give some brief results for their -versions.
Keywords
Cite
@article{arxiv.2102.00139,
title = {The deranged Bell numbers},
author = {Hacéne Belbachir and Yahia Djemmada and László Németh},
journal= {arXiv preprint arXiv:2102.00139},
year = {2021}
}