Isomorphisms between pattern classes

Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure, including their enumeration, is determined.

[1]  Rebecca Smith,et al.  Permutation Reconstruction , 2006, Electron. J. Comb..

[2]  Rodica Simion,et al.  Restricted Permutations , 1985, Eur. J. Comb..