
332 Commutation Relations, Normal Ordering, and Stirling Numbers
The mapping ρ → ρ
is seen to be an involution of A which is not defined in the case
when the block C is either of the following forms:
(i) C = {E
1
,...,E
t
, {c
2
γ
2
}, {c
1
γ
1
}}, (ii) C = {E
1
,...,E
t
, {c
1
γ
1
c
2
γ
2
}},
where γ
1
and γ
2
are possibly empty sequences and the E
i
are contents-ordered blocks which
occur in decreasing order according to the size of the first element and in which the first
element is also the smallest one within each block. However, exchanging (i)for(ii), and
vice versa, defines an involution in this case that reverses the weight, which completes the
proof of (8.122).
8.5.10.2 Com ...