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A117107
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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).
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2
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1, 1, 3, 12, 57, 304, 1765, 10943, 71519, 488186, 3456526, 25251479, 189545179
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OFFSET
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1,3
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COMMENTS
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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)
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LINKS
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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.
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EXAMPLE
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See example in A137546.
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CROSSREFS
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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
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KEYWORD
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nonn,more
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AUTHOR
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Steve Butler, Apr 18 2006
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STATUS
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approved
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