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This paper completes a project to enumerate permutations avoiding a triple Tof 4-letter patterns, in the sense of classical pattern avoidance, for every T.There are 317 symmetry classes of such triples T and previous papers haveenumerated avoiders for all but 14 of them. One of these 14 is conjectured notto have an algebraic generating function. Here, we find the generating functionfor each of the remaining 13, and it is algebraic in each case.

Enumeration of permutations avoiding a triple of 4-letter patterns is all done