Hostname: page-component-5db58dd55d-8lnk4 Total loading time: 0 Render date: 2026-05-30T23:32:18.698Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Upper Bound for 1324-Avoiding Permutations

Published online by Cambridge University Press:  09 July 2014

MIKLÓS BÓNA
MIKLÓS BÓNA*
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611–8105, USA (e-mail: bona@ufl.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that the number of 1324-avoiding permutations of length n is less than $(7+4\sqrt{3})^n$. The novelty of our method is that we injectively encode such permutations by a pair of words of length n over a finite alphabet that avoid a given factor.

Keywords

Primary 05A15Secondary 05A0505A1605A20

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 5: Honouring the Memory of Philippe Flajolet - Part 1 , September 2014 , pp. 717 - 724
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Albert, M. H., Elder, M., Rechnitzer, A., Westcott, P. and Zabrocki, M. (2006) On the Stanley–Wilf limit of 4231-avoiding permutations and a conjecture of Arratia. Adv. Appl. Math. 36 96–105.Google Scholar
[2]Arratia, R. (1999) On the Stanley–Wilf conjecture for the number of permutations avoiding a given pattern. Electron. J. Combin. 6 #1.Google Scholar
[3]Bóna, M. (2007) New records in Stanley–Wilf limits. Europ. J. Combin. 28 75–85.CrossRefGoogle Scholar
[4]Bóna, M. (2012) Combinatorics of Permutations, second edition, CRC Press/Chapman & Hall.Google Scholar
[5]Claesson, A., Jelinek, V. and Steingrímsson, E. (2012) Upper bounds for the Stanley–Wilf limit of 1324 and other layered patterns. J.Combin. Theory Ser. A 119 1680–1691.CrossRefGoogle Scholar
[6]Flajolet, P. and Sedgewick, R. (2009) Analytic Combinatorics, Cambridge University Press.CrossRefGoogle Scholar
[7]Marcus, A. and Tardos, G. (2004) Excluded permutation matrices and the Stanley–Wilf conjecture. J. Combin. Theory Ser. A 107 153–160.CrossRefGoogle Scholar
[8]Simion, R. and Schmidt, F. (1985) Restricted permutations. Europ. J. Combin. 6 383–406.CrossRefGoogle Scholar