14,422 research outputs found
Path count asymptotics and Stirling numbers
We obtain formulas for the growth rate of the numbers of certain paths in
infinite graphs built on the two-dimensional Eulerian graph. Corollaries are
identities relating Stirling numbers of the first and second kinds.Comment: Misprint corrected. To appear in Proc. Amer. Math. So
Normal Ordering for Deformed Boson Operators and Operator-valued Deformed Stirling Numbers
The normal ordering formulae for powers of the boson number operator
are extended to deformed bosons. It is found that for the `M-type'
deformed bosons, which satisfy , the
extension involves a set of deformed Stirling numbers which replace the
Stirling numbers occurring in the conventional case. On the other hand, the
deformed Stirling numbers which have to be introduced in the case of the
`P-type' deformed bosons, which satisfy , are found to depend on the operator . This distinction
between the two types of deformed bosons is in harmony with earlier
observations made in the context of a study of the extended
Campbell-Baker-Hausdorff formula.Comment: 14 pages, Latex fil
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