English

On Bell numbers of type $D$

Combinatorics 2025-04-24 v1

Abstract

In this paper, we will introduce Bell numbers D(n)D(n) of type DD as an analogue to the classical Bell numbers related to all the partitions of the set [n][n]. Then based on a signed set partition of type DD, we will construct the recurrence relations of Bell numbers D(n)D(n). In addition, we deduce the exponential generating function for D(n)D(n). Finally, we will provide an explicit formula for D(n)D(n).

Keywords

Cite

@article{arxiv.2504.16522,
  title  = {On Bell numbers of type $D$},
  author = {Hasan Arslan and Nazmiye Alemdar and Mariam Zaarour and Hüseyin Altındiş},
  journal= {arXiv preprint arXiv:2504.16522},
  year   = {2025}
}
R2 v1 2026-06-28T23:08:15.496Z