
208 Commutation Relations, Normal Ordering, and Stirling Numbers
• A combinatorial interpretation for the normal ordering coefficients S
2,2
(n, k)arising
from (X
2
D
2
)
n
was mentioned in Example 4.8; see [106, Section 4.2] for more in-
formation. An extension to the case of (X
r
D
r
)
n
for arbitrary r ∈ N can be found
in [106, Section 4.3].
• Normal ordering (X+D)
n
is closely related to (bicolored) involutions; see [106, Section
3.3]. As evidence for this connection, note that the coefficients in (6.12) enumerate
bicolored involutions; see [106, Proposition 2] for a more precise statement. In [106],
one can also find combinatorial interpretations for the normal ordering ...