
In One Line and Close. Permutations as Linear Orders. 33
PROOF Let us assume the contrary, that is, that there exists an n-
permutation p so that each maximum-length alternating subsequence of p
avoids the entry n. This means that all maximum-length alternating subse-
quences of p start on the right of n,orendontheleftofn, or “skip” n;that
is, contain an entry on the left of n that is followed by an entry on the right
of n. It is easy to see that each of these three kinds of subsequences can be
transformed into an alternating subsequence of the same length that contains
n. For instance, if s is an alternating subsequence of p so that a<bare two
consecutive ...