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A137536
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Number of permutations in S_n avoiding {bar 4}2153 (i.e., every occurrence of 2153 is contained in an occurrence of a 42153).
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3
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1, 1, 2, 6, 23, 104, 532, 3002, 18375, 120559, 840480, 6184729, 47788384, 386126534, 3251434927, 28454039404
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OFFSET
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0,3
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COMMENTS
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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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EXAMPLE
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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