Normal ordering problem and the extensions of the Stirling grammar
Shi-Mei Ma, Toufik Mansour, Matthias Schork
TL;DR
This paper explores the relationship between context-free grammars and the normal ordering problem, extending Stirling grammar to characterize combinatorial sequences like generalized Stirling numbers and r-Dowling polynomials.
Contribution
It provides grammatical characterizations of well-known combinatorial sequences and extends Stirling grammar to new combinatorial structures.
Findings
Characterization of generalized Stirling numbers via grammar
Extension of Stirling grammar to r-Dowling polynomials
Discussion of future research directions
Abstract
The purpose of this paper is to investigate the connection between context-free grammars and normal ordering problem, and then to explore various extensions of the Stirling grammar. We present grammatical characterizations of several well known combinatorial sequences, including the generalized Stirling numbers of the second kind related to the normal ordering problem and the -Dowling polynomials. Also, possible avenues for future research are described.
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