
270 Commutation Relations, Normal Ordering, and Stirling Numbers
Theorem 7.63 (Diaz, Pariguan) Let n ∈ N.Ifn ≥ 2, then the normal ordering coeffi-
cients N(A, k, q) of V
a
1
U
b
1
···V
a
n
U
b
n
in MA
h|q
are given by
N(A, k, q)=
p k
n−1
i=1
c(b
i
, |a
>i
| + |p
>i
|,p
i
),
where the partition p of k must be such that 0 ≤ p
i
≤ b
i
for i ∈ [n −1].
As in the undeformed case, one may also consider antinormal ordering formulas. It seems
that the first such result was (7.95), which appeared in [1033]. In [1184], relations (7.95)
and (7.96) were shown. These results constitute the analog of Proposition 7.60.
Proposition 7.64 (Stafford, Zhang; Zhang, Wang) In MA
h|q
one has for all n ∈