Claesson, Anders and Jelínek, Vít and Steingrimsson, Einar (2012) Upper bounds for the Stanley–Wilf limit of 1324 and other layered patterns. Journal of Combinatorial Theory Series A, 119 (8). pp. 1680-1691. ISSN 0097-3165
Full text not available in this repository. (Request a copy from the Strathclyde author)Abstract
We prove that the Stanley-Wilf limit of any layered permutation pattern of length l is at most 4l(2), and that the Stanley-Wilf limit of the pattern 1324 is at most 16. These bounds follow from a more general result showing that a permutation avoiding a pattern of a special form is a merge of two permutations, each of which avoids a smaller pattern. We also conjecture that, for any k >= 0, the set of 1324-avoiding permutations with k inversions contains at least as many permutations of length n + 1 as those of length n. We show that if this is true then the Stanley-Wilf limit for 1324 is at most e(pi root 2/3) similar or equal to 13.001954.
| Item type: | Article |
|---|---|
| ID code: | 42133 |
| Keywords: | upper bounds , stanley-wilf limit , layered patterns, pattern avoidance, layered permutations , Electronic computers. Computer science |
| Subjects: | Science > Mathematics > Electronic computers. Computer science |
| Department: | Faculty of Science > Computer and Information Sciences |
| Related URLs: | |
| Depositing user: | Pure Administrator |
| Date Deposited: | 19 Nov 2012 14:20 |
| Last modified: | 15 Dec 2012 16:37 |
| URI: | http://strathprints.strath.ac.uk/id/eprint/42133 |
Actions (login required)
| View Item |