  We improve the lower bound on the number of permutations of {1,2,...,n} in
which no 3-term arithmetic progression occurs as a subsequence, and derive
lower bounds on the upper and lower densities of subsets of the positive
integers that can be permuted to avoid 3-term and 4-term APs. We also show that
any permutation of the positive integers must contain a 3-term AP with odd
common difference as a subsequence, and construct a permutation of the positive
integers that does not contain any 4-term AP with odd common difference.
