
The q-Deformed Weyl Algebra and the Meromorphic Weyl Algebra 275
Let us assume that the pairs within a member of A
n,3
are arranged from left-to-right in
decreasing order according to the size of the larger element. Then the generic (i
1
,i
2
)-term in
the sum on the right-hand side of (7.106), where 1 ≤ i
1
≤ i
2
≤ n, counts all of the members
of A
n,3
in which the element 2 belongs to the (n −i
2
+ 1)th left-most pair and the element 1
belongs to the (n −i
1
+ 2)-nd left-most pair. To see this, note that there are
n−1
j=i
2
(2j +1)
possibilities for the n − i
2
pairs lying to the left of the pair containing the 2 (starting with
the one containing 2n + 2, which is alwa ...