TY - JOUR
T1 - Finite transition matrices for permutations avoiding pairs of length four patterns
AU - Kremer, Darla
AU - Shiu, Wai Chee
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
PY - 2003/7/6
Y1 - 2003/7/6
N2 - 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)|.
AB - 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)|.
KW - Forbidden subsequences
KW - Pattern avoiding permutations
KW - Restricted permutations
UR - http://www.scopus.com/inward/record.url?scp=84867934467&partnerID=8YFLogxK
U2 - 10.1016/S0012-365X(03)00042-6
DO - 10.1016/S0012-365X(03)00042-6
M3 - Journal article
AN - SCOPUS:84867934467
SN - 0012-365X
VL - 268
SP - 171
EP - 183
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -