A general upper bound in extremal theory of sequences
We investigate the extremal function which, for a given finite sequence over symbols, is defined as the maximum length of a sequence of integers such that 1) , 2) implies and 3) contains no subsequence of the type . We prove that is very near to be linear in for any fixed of length greater than 4, namely that Here is the length of and is the inverse to the Ackermann function and goes to infinity very slowly. This result extends the estimates in [S] and [ASS] which...