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A137557 Number of permutations in S_n avoiding 345{bar 2}{bar 1} (i.e., every occurrence of 345 is contained in an occurrence of a 34521). 0
1, 2, 5, 14, 43, 150, 617, 3050, 18059, 125930, 1013553, 9246862, 94226123, 1059882190, 13035332841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..15.

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

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

CROSSREFS

Sequence in context: A137554 A137555 A137556 * A306799 A148335 A268419

Adjacent sequences:  A137554 A137555 A137556 * A137558 A137559 A137560

KEYWORD

nonn,more

AUTHOR

Lara Pudwell, Apr 25 2008

EXTENSIONS

a(8)-(15) from Lars Blomberg, Jun 06 2018

STATUS

approved

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Last modified July 5 05:10 EDT 2022. Contains 355087 sequences. (Running on oeis4.)