A generalized Davenport–Schinzel sequence is one over a finite alphabet that excludes subsequences isomorphic to a fixed forbidden subsequence. The fundamental problem in this area is bounding the maximum length of such sequences. Following Klazar, we let Ex(σ, n) be the maximum length of a sequence over an n-letter alphabet excluding subsequences isomorphic to σ. It has been proved that for every σ, Ex(σ, n) is either linear or very close to linear. In particular it is O(n2α(n) O(1) ), where… CONTINUE READING