where # A is used to denote the cardinality of a set A. The next result of this type was discovered by Rotem [11]. He showed that the set of (1 E Sn which do not have either 231 or 312 patterns has cardinality 2n -1. And, finally, the definitive solution to the problem is to be found in a recent paper by Simion and Schmidt [12]. Given any set A s; S3, they have determined the number of permutations in Sn which avoid A. In view of the preceding remarks, a natural question arises: Rather than… CONTINUE READING