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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
94 Commutation Relations, Normal Ordering, and Stirling Numbers
Theorem 4.35 (M´endez, Rodr´ıguez) For al l s
1
k ≤|s|, one has that
S
r,s|q
(k)=
(1)
k
k!
k
p=s
1
(1)
p
q
(
kp
2
)
k
p
q
n
m=1
[d
m1
+ p]
s
m
|q
. (4.41)
In the uniform case, (4.41) reduces to (4.30) for r = s .
endez and Rodr´ıguez [808, 809] gave an interpretation in terms of colonies and bugs,
where certain q-weights are introduced. In addition to the terminology introduced above,
we call a bug of type (r, s)aworm if s = 0 (that is, it has no legs). When constructing a
colony, after placing all the bugs, a ghost bug is placed. Its legs do not cross among them
and occupy all the empty cells of the
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Publisher Resources

ISBN: 9781466579897