Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T21:12:15.757Z Has data issue: false hasContentIssue false

Growing at a Perfect Speed

Published online by Cambridge University Press:  01 May 2009

M. H. ALBERT
Affiliation:
Department of Computer Science, University of Otago, Dunedin, New Zealand (e-mail: malbert@cs.otago.ac.nz)
S. A. LINTON
Affiliation:
Centre for Interdisciplinary Research in Computational Algebra, University of St Andrews, Fife, Scotland (e-mail: sal@dcs.st-and.ac.uk)

Abstract

A collection of permutation classes is exhibited whose growth rates form a perfect set, thereby refuting some conjectures of Balogh, Bollobás and Morris.

Type
Paper
Copyright
Copyright © Cambridge University Press 2009

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.)

References

[1]Albert, M. H. (2007) On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation. Random Struct. Alg. 31 227238.CrossRefGoogle Scholar
[2]Albert, M. H., Atkinson, M. D. and Ruškuc, N. (2003) Regular closed sets of permutations. Theoret. Comput. Sci. 306 85100.CrossRefGoogle Scholar
[3]Balogh, J., Bollobás, B. and Morris, R. (2006) Hereditary properties of ordered graphs. In Topics in Discrete Mathematics, Vol. 26 of Algorithms Combin., Springer, Berlin, pp. 179213.CrossRefGoogle Scholar
[4]Delgado, M., Linton, S. and Morais, J. (2007) Automata: A GAP package (1.10). http://cmup.fc.up.pt/cmup/mdelgado/automata/Google Scholar
[5]GAP: Groups, Algorithms, and Programming, Version 4.4.10 (2007). http://www.gap-system.orgGoogle Scholar
[6]Huczynska, S. and Vatter, V.Grid classes and the Fibonacci dichotomy for restricted permutations. Electron. J. Combin. 13 #54 (electronic).Google Scholar
[7]Kaiser, T. and Klazar, M. (2002/03) On growth rates of closed permutation classes. Electron. J. Combin. 9 #10 (electronic).Google Scholar
[8]Marcus, A. and Tardos, G. (2004) Excluded permutation matrices and the Stanley–Wilf conjecture. J. Combin. Theory Ser. A 107 153160.CrossRefGoogle Scholar
[9]Vatter, V. Small permutation classes (preprint) arXiv:0712.4006v2 [Math.CO].Google Scholar