  Permutations of the positive integers avoiding arithmetic progressions of
length $5$ were constructed in (Davis et al, 1977), implying the existence of
permutations of the integers avoiding arithmetic progressions of length $7$. We
construct a permutation of the integers avoiding arithmetic progressions of
length $6$. We also prove a lower bound of $\frac{1}{2}$ on the lower density
of subsets of positive integers that can be permuted to avoid arithmetic
progressions of length $4$, sharpening the lower bound of $\frac{1}{3}$ from
(LeSaulnier and Vijay, 2011). In addition, we generalize several results about
forbidden arithmetic progressions to construct permutations avoiding
generalized arithmetic progressions.
