  We introduce a new method for encoding permutations as weighted independent
sets in a family of graphs we call cores. The encoding allows us to enumerate
(1324, 2143)-, (1234, 1324, 2143)-, (1234, 1324, 1432, 3214)-avoiding
permutations with respect to their number of "boundary points" and the size of
the independent set in the graph they correspond to.
