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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
322 Commutation Relations, Normal Ordering, and Stirling Numbers
and Proposition 8.106 were also generalized in [997, Theorem 2.3]. The last property we
mention is the generalization of (8.91). Using generalized factorials, we can write [997,
Theorem 2.2] as
(x +(a + b)r|−a)
n
=
n
k=0
G
a;b
(n, k; r)(x|b)
k
.
8.5.6 Interpretation in Terms of Rooks
In addition to the above combinatorial interpretation, we can relate the generalized
Stirling numbers S
s;1
(n, k)fors N
0
to the s-rook numbers introduced by Goldman and
Haglund [485]; see Section 2.4.4.3. This connection generalizes the well-known interpretation
of the Stirling numbers of the second kind as particular rook numbers; see Corollary 2.56.
For s = 0 corresponding to the Weyl algebra generated by variables ...
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Publisher Resources

ISBN: 9781466579897