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A137549
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Number of permutations in S_n avoiding 5{bar 1}{bar 2}43 (i.e. every occurrence of 543 is contained in an occurrence of a 51243).
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0
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1, 2, 5, 14, 43, 143, 511, 1950, 7903, 33848, 152529, 720466, 3555715, 18285538, 97752779, 542107657, 3112916651, 18477588573, 113203102619, 714836382820, 4646688247467, 31057662848411, 213217403924667, 1502038027665181
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Comment from Lara Pudwell (Lara.Pudwell(AT)valpo.edu), 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
| Lara Pudwell, Enumeration Schemes for Pattern-Avoiding Words and Permutations, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008.
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CROSSREFS
| Sequence in context: A006789 A202060 A098569 * A014327 A173437 A137550
Adjacent sequences: A137546 A137547 A137548 * A137550 A137551 A137552
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KEYWORD
| nonn
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AUTHOR
| Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Apr 25 2008
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