A poset is {\it (\3+\1)-free} if it contains no induced subposet isomorphic
to the disjoint union of a 3-element chain and a 1-element chain. These posets
are of interest because of their connection with interval orders and their
appearance in the (\3+\1)-free Conjecture of Stanley and Stembridge. The
dimension 2 posets P are exactly the ones which have an associated
permutation π where i≺j in P if and only if i<j as integers and
i comes before j in the one-line notation of π. So we say that a
permutation π is {\it (\3+\1)-free} or {\it (\3+\1)-avoiding} if its
poset is (\3+\1)-free. This is equivalent to π avoiding the permutations
2341 and 4123 in the language of pattern avoidance. We give a complete
structural characterization of such permutations. This permits us to find their
generating function.Comment: 17 page