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- W1974697531 abstract "Some years ago Gessel [8] gave a q -analogue of the celebrated exponential formula. We present a new combinatorial interpretation of this formula, and apply it to give q -analogues of Bell numbers and Stirling numbers of the first and second kinds. Curiously, the q -Stirling numbers of the second kind obtained in this way are different from the existing q -Stirling numbers of the second kind, but the q -Stirling numbers of the first kind are the same. We further consider q -analogues of the iterated exponential integers. Il y a quelques années, Gessel [8] a donné un q -analogue de la célèbre formule exponentielle. Nous présentons une nouvelle interprétation combinatoire de cette formule et son application menant à des q -analogues des nombres de Bell et des nombres de Stirling de la première et seconde espèce. Il est intéressant de remarquer que les nombres q -Stirling de la seconde espèce ainsi obtenus diffèrent de ceux déj'a parus dans la litérature, tandis que ceux de la première espèce sont les mêmes. Nous considérons aussi des q -analogues des entiers dont la fonction génératrice est une exponentielle itérée." @default.
- W1974697531 created "2016-06-24" @default.
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- W1974697531 date "1996-10-01" @default.
- W1974697531 modified "2023-09-29" @default.
- W1974697531 title "Some applications of the q-exponential formula" @default.
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- W1974697531 doi "https://doi.org/10.1016/s0012-365x(96)83016-0" @default.
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