Enumerative Combinatorics presents elaborate and systematic coverage of the theory of
enumeration. The first seven chapters provide the necessary background, including basic …

Mathematics is the science of patterns, and mathematicians attempt to understand these
patterns and discover new ones using a variety of tools. In Proofs That Really Count, award …

Commutation Relations, Normal Ordering, and Stirling Numbers Page 1 Commutation
Relations, Normal Ordering, and Stirling Numbers Toufik Mansour • Matthias Schork Mansour • …

In recent years, some degenerate versions of quite a few special numbers and polynomials
are introduced and investigated by means of various methods. The aim of this paper is to …

It is known that the unsigned Stirling numbers of the first kind are related to normal ordering
in the shift algebra. The aim of this paper is to consider the-shift algebra, which is a …

In 2008, Spivey found a recurrence relation for the Bell numbers. We consider the
probabilistic-Bell polynomials associated with,, which are a probabilistic extension of the …

Broder introduced the-Stirling numbers of the first kind and of the second kind which
enumerate restricted permutations and respectively restricted partitions, the restriction being …

Let G be a finite group of order m≥ 1. A Dowling lattice Qn (G) is the geometric lattice of rank
n over G. In this paper, we define the r-Whitney numbers of the first and second kind over Qn …

The notion of r-Stirling numbers implies the definition of generalized Bell (or r-Bell) numbers.
The r-Bell numbers have appeared in several works, but there is no systematic treatise on …

In the paper, after concisely surveying some closed formulas and applications of special
values of the Bell polynomials of the second kind for some special sequences and …