We show that the four classes of pattern avoiding permutations, S n(1234,3214), S n(4123,3214), S n(2341,2143) and S n(1234,2143) are enumerated by the formula (4 n-1+2)/3. In an electronic appendix we provide finite transition matrices for the number |S n(u,v)| of permutations avoiding pairs (u,v) of length four patterns where u contains the subsequence 123 and v contains the subsequence 321 as well as a transition matrix for |S n(1234,43215)|.
Scopus Subject Areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Forbidden subsequences
- Pattern avoiding permutations
- Restricted permutations