Geodesic
On Ore-Stirling numbers defined by normal ordering in the Ore algebra
Filomat, Tome 37 (2023) no. 18, p. 6115

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DOI

Normal ordering in theWeyl algebra is related to the Stirling numbers of the second kind, while normal ordering in the shift algebra is related to the unsigned Stirling numbers of the first kind. The Ore algebra – this name was introduced recently by Patrias and Pylyavskyy – is an algebra closely related to the Weyl algebra and the shift algebra. We consider a two-parameter family of generalized Ore algebras which comprises all algebras mentioned by specializing the parameters suitably. Analogs of the Stirling numbers – called Ore-Stirling numbers – are introduced as normal ordering coefficients in the generalized Ore algebra. In the limit where one parameter vanishes they reduce to the Stirling numbers of the second kind or the unsigned Stirling numbers of the first kind. Choosing the parameters appropriately, a oneparameter family of Ore-Stirling numbers interpolating between Stirling numbers of the second kind and unsigned Stirling numbers of the first kind is found. Several properties of the Ore-Stirling numbers as well as the associated Ore-Bell numbers are discussed.
DOI : 10.2298/FIL2318115M
Classification : 05A10, 05A15, 11B73, 16S15
Keywords: Weyl algebra, Shift algebra, Ore algebra, Stirling number, Bell number, Normal ordering 
Toufik Mansour; Matthias Schork. On Ore-Stirling numbers defined by normal ordering in the Ore algebra. Filomat, Tome 37 (2023) no. 18, p. 6115 . doi: 10.2298/FIL2318115M
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     title = {On {Ore-Stirling} numbers defined by normal ordering in the {Ore} algebra},
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