
In This Way, but Nicely. Pattern Avoidance. Follow-Up. 217
DEFINITION 5.35 For any positive integer n,letk
n
be the positive
integer for which
M
n
=max
kn
M
k
+ k
m
2
is maximal. If there are several integers with this property, then let k
n
be the
largest among them.
In other words, k
n
is the largest possible length of the remaining permu-
tation after removing the last layer of an optimal n-permutation p.When
there is no danger of confusion, we will only write k instead of k
n
, to simplify
notation. We will also always use m = n − k to denote the length of the last
layer of p.
We continue our search for 132-optimal n-permutations. The construction
at the beginni ...