Deflatability of Permutation Classes
  A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee non-deflatability are proved and examples of both deflatable and non-deflatable principal classes are given. 
M. H. Albert, M. D. Atkinson, Cheyne Homberger, Jay Pantone
math.CO