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Commutation Relations, Normal Ordering, and Stirling Numbers
book

Commutation Relations, Normal Ordering, and Stirling Numbers

by Toufik Mansour, Matthias Schork
September 2015
Intermediate to advanced content levelIntermediate to advanced
528 pages
19h 34m
English
Chapman and Hall/CRC
Content preview from Commutation Relations, Normal Ordering, and Stirling Numbers
302 Commutation Relations, Normal Ordering, and Stirling Numbers
As the expression for the generalized Stirling numbers S
s;h
(n, k) given in Proposi-
tion 8.43 shows, they are closely related to the generalized Stirling numbers S(s +1;n, k)=
S
s+1,1
(n, k). The generalized Stirling numbers defined by (8.50) are also very natural insofar
as many properties of the conventional Stirling numbers of the second kind have a simple
analog. For example, the interpretation of S(n, k) as rook number of a staircase Ferrers
board (see Corollary 2.56) generalizes in a beautiful way to the interpretation of S
s;h
(n, k)
as s-rook number of the staircase board (see Theorem 8.110). Although we defined S
s;h
(n, k)
above for s N
0
(to conform with the interpretation of U
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Publisher Resources

ISBN: 9781466579897