This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A137546 Number of permutations in S_n avoiding 5234{bar 1} (i.e., every occurrence of 5234 is contained in an occurrence of a 52341). 13
 1, 2, 6, 23, 104, 535, 3082, 19763, 140885, 1117101, 9853890, 96543043, 1046549545, 12480046880, 162595262990 (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 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. EXAMPLE a(5) = 104: There are 16 permutations that have a 5234 *pattern* that is not followed by a 1. This is different from looking for the string 5234 followed by 1. A 5234 pattern is a string of 4 numbers abcd where b

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)