A137548 Number of permutations in S_n avoiding {bar 5}1234 (i.e., every occurrence of 1234 is contained in an occurrence of a 51234).

1, 1, 2, 6, 23, 104, 535, 3088, 19937, 144065, 1165109, 10518741, 105460057, 1166159683, 14117684632, 185784598853

Offset

0,3

Comments

From Lara Pudwell, Oct 23 2008: (Start)

A permutation p avoids a pattern q if it has no subsequence that is order-isomorphic to q. For example, p avoids the pattern 132 if it has no subsequence abc with a < c < b.

Barred pattern avoidance considers permutations that avoid a pattern except in a special case. Given a barred pattern q, we may form two patterns, q1 = the sequence of unbarred letters of q and q2 = the sequence of all letters of q.

A permutation p avoids barred pattern q if every instance of q1 in p is embedded in a copy of q2 in p. In other words, p avoids q1, except in the special case that a copy of q1 is a subsequence of a copy of q2.

For example, if q = 5{bar 1}32{bar 4}, then q1 = 532 and q2 = 51324. p avoids q if every for decreasing subsequence acd of length 3 in p, one can find letters b and e so that the subsequence abcde of p has b < d < c < e < a. (End)

Links

Table of n, a(n) for n=0..15.

Lara Pudwell, Enumeration Schemes for Pattern-Avoiding Words and Permutations, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008.

Lara Pudwell, Enumeration schemes for permutations avoiding barred patterns, El. J. Combinat. 17 (1) (2010) R29.

Example

See example in A137546.

Crossrefs

Cf. A137546.

Sequence in context: A137545 A137546 A137547 * A080108 A113227 A200406

Adjacent sequences: A137545 A137546 A137547 * A137549 A137550 A137551

Keyword

nonn,more

Author

Lara Pudwell, Apr 25 2008

Extensions

a(8)-(15) from Lars Blomberg, Jun 05 2018

a(0)=1 prepended by Alois P. Heinz, Jul 10 2023

Status

approved