  In this paper, we study pattern avoidance for stabilized-interval-free (SIF)
permutations. These permutations are contained in the set of indecomposable
permutations and in the set of derangements. We enumerate pattern-avoiding SIF
permutations for classical and pairs of patterns of size 3. In particular, for
the patterns 123 and 231, we rely on combinatorial arguments and the
fixed-point distribution of general permutations avoiding these patterns. We
briefly discuss 123-avoiding permutations with two fixed points and offer a
conjecture for their enumeration by the distance between their fixed points.
For the pattern 231, we also give a direct argument that uses a bijection to
ordered forests.
