A137537 - OEIS

%I #20 Jul 10 2023 12:13:47

%S 1,1,2,6,23,104,532,3003,18400,120960,845823,6249642,48539947,

%T 394620211,3346466726,29516055880

%N Number of permutations in S_n avoiding 5134{bar 2} (i.e., every occurrence of 5134 is contained in an occurrence of a 51342).

%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 Lara Pudwell, <a href="https://doi.org/10.37236/301">Enumeration schemes for permutations avoiding barred patterns</a>, El. J. Combinat. 17 (1) (2010) R29.

%e See example in A137546.

%Y Cf. A137546.

%K nonn,more

%O 0,3

%A _Lara Pudwell_, Apr 25 2008

%E a(8)-(15) from _Lars Blomberg_, Jun 04 2018

%E a(0)=1 prepended by _Alois P. Heinz_, Jul 10 2023