Classification of Forbidden Subsequences of Length 4

We complete the classification of forbidden subsequences of length 4 by resolving the last open question concerning thesymmetry classesof (1234) and (4123). Our method is to construct specificswitchingoperations onSn(123) which partition its elements intoequivalence classes.This and the fact that the treeT(123) can be embedded nicely inT(1234) andT(4123) lead to the conclusion that |Sn(1234)|= |Sn(4123)| for alln∈N.