A117107 Number of permutations in S_n avoiding 21{bar 3}54 (i.e., every occurrence of 2154 is contained in an occurrence of a 21354) and such that the graph corresponding to the permutation is connected (see "Forest-like permutations" below).

1, 1, 3, 12, 57, 304, 1765, 10943, 71519, 488186, 3456526, 25251479, 189545179

Offset

1,3

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=1..13.

M. Bousquet-Mélou and S. Butler, Forest-like permutations, arXiv:math/0603617 [math.CO], 2006.

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

Example

See example in A137546.

Crossrefs

Cf. A137536, A137537, A137538, A137539, A137540, A137541, A137542, A137543, A137544, A137545, A137546, A137547, A137548.

Sequence in context: A103370 A094149 A291695 * A159609 A128326 A323631

Adjacent sequences: A117104 A117105 A117106 * A117108 A117109 A117110

Keyword

nonn,more

Author

Steve Butler, Apr 18 2006

Status

approved