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 A137555 Number of permutations in S_n avoiding {bar 4}{bar 5}123 (i.e., every occurrence of 123 is contained in an occurrence of a 45123). 0

%I

%S 1,2,5,14,43,147,578,2702,15252,103150,817928,7428844,75807522,

%T 856512850,10596715538

%N Number of permutations in S_n avoiding {bar 4}{bar 5}123 (i.e., every occurrence of 123 is contained in an occurrence of a 45123).

%C From _Lara Pudwell_, Oct 23 2008: (Start)

%C 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.

%C 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.

%C 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.

%C 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)

%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/papers/pudwell_thesis.pdf">Enumeration Schemes for Pattern-Avoiding Words and Permutations</a>, Ph. D. Dissertation, Math. Dept., Rutgers University, May 2008.

%H L. Pudwell, <a href="http://www.emis.de/journals/EJC/Volume_17/Abstracts/v17i1r29.html">Enumeration schemes for permutations avoiding barred patterns</a>, El. J. Combinat. 17 (1) (2010) R29.

%K nonn,more

%O 1,2

%A _Lara Pudwell_, Apr 25 2008

%E a(8)-(15) from _Lars Blomberg_, Jun 06 2018

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Last modified July 6 04:31 EDT 2022. Contains 355108 sequences. (Running on oeis4.)