1,2

321- 2143-avoiding permutations of length n are in one-to-one correspondence with simple Dyck paths of semilength n (a Dyck path is simple if it has at most one long upward edge or at most one long downward edge, an edge being "long" if it consists of at least two steps). They are the Grassmannian permutations and their inverses. They can also be characterized as those permutations whose essential set is contained in one row or one column. This sequence also enumerates the cyclic arrangements of 1, 2, ... n+1 which avoid the cyclic arrangement 1234.

Also, number of 1324-avoiding circular permutations on [n+1].

S. Billey, W. Jockusch and R.P. Stanley. Some combinatorial properties of Schubert polynomials, Journal of Algebraic Combinatorics 2(4):345-374, 1993

K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. Duke Mathematical Journal 85(1):61-76, 1996.

A. Vella. Pattern avoidance in permutations: linear and cyclic orders, Electron. J. Combin. 9 (2002/03), no. 2, Research paper 18, 43 pp.

D. Callan, Pattern avoidance in circular permutations.

2^(i+1) - binomial(i+1, 3) - 2i - 1

G.f.= x(2x^4-5x^3+7x^2-4x+1)/[(1-2x)(1-x)^4]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2004

Cf. A000325.

Sequence in context: A108890 A027929 A001659 this_sequence A005183 A005348 A067676

Adjacent sequences: A088918 A088919 A088920 this_sequence A088922 A088923 A088924

easy,nonn

Antoine Vella (avella(AT)math.uwaterloo.ca), Oct 23 2003