

A137538


Number of permutations in S_n avoiding 25{bar 1}34 (i.e., every occurrence of 2534 is contained in an occurrence of a 25134).


1



1, 1, 2, 6, 23, 104, 532, 3004, 18426, 121393, 851810, 6325151, 49448313, 405298482, 3470885747, 30965656442, 287083987270, 2759838731485, 27458514900626, 282264050120512, 2993392570828096, 32704759586810036, 367673428857985261
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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 orderisomorphic 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)
The number of permutations of length n avoiding the dashed pattern 1423.  Andrew Baxter, May 17 2011
Apparently, also the number of permutations of length n avoiding the barred pattern 23{bar 1}54, which are the same as the permutations avoiding dashed pattern 1243.  Andrew Baxter, May 17 2011


LINKS

Table of n, a(n) for n=1..23.
A. M. Baxter, Algorithms for Permutation Statistics, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2011.
Andrew M. Baxter and Lara K. Pudwell, Enumeration schemes for dashed patterns, arXiv preprint arXiv:1108.2642 [math.CO], 2011.
Lara Pudwell, Enumeration Schemes for PatternAvoiding 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.


EXAMPLE

See example in A137546.


CROSSREFS

Cf. A110447, A113226, A137546.
Sequence in context: A030266 A137536 A137537 * A137539 A137540 A137541
Adjacent sequences: A137535 A137536 A137537 * A137539 A137540 A137541


KEYWORD

nonn


AUTHOR

Lara Pudwell, Apr 25 2008


EXTENSIONS

Edited by Andrew Baxter, May 17 2011


STATUS

approved



