Enumerating permutations that avoid three term arithmetic progressions

Abstract

It is proved that the number of permutations of the set {1, 2, 3, . . . , n} that avoid three term arithmetic progressions is at most (2.7)n/21 for n ≥ 11 and at each end of any such permutation, at least n/2 - 6 entries have the same parity.