On Bell numbers of type D

2025/04/23 by Arslan, Hasan, Alemdar, Nazmiye, Zaarour, Mariam +1
#05A05 #05A15 #05A18 #05A19 #11B73 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.16522

Abstract

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

Related

• The deranged Bell numbers
• Combinatorial and Arithmetical Properties of the Restricted and\n Associated Bell and Factorial Numbers
• Sets of iterated Partitions and the Bell iterated Exponential Integers
• Partial Deranged Bell Numbers and Their Combinatorial Properties
• Set Partitions and Other Bell Number Enumerated Objects