Finite transition matrices for permutations avoiding pairs of length four patterns Original Research Article

We show that the four classes of pattern avoiding permutations, Sn(1234,3214), Sn(4123,3214), Sn(2341,2143) and Sn(1234,2143) are enumerated by the formula (4n−1+2)/3. In an electronic appendix we provide finite transition matrices for the number |Sn(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 |Sn(1234,43215)|.