Recent developments in combinatorial aspects of normal ordering

Abstract

In this paper, we report on recent progress concerning combinatorial aspects of normal ordering. After giving a short introduction to the history and motivation of normal ordering, we present some recent developments. Many of them are related to the quantum plane or the Weyl algebra or close relatives thereof. Along the way, a few open problems are mentioned. 2020 Mathematics Subject Classification: 05A05; 05A10; 05A15; 05A19; 05C20; 05C30; 11B73, 11B75; 13N15; 16S15; 16S32; 16T30