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Permutations Sortable by n – 4 Passes Through a Stack

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Abstract

We characterise and enumerate permutations that are sortable by n – 4 passes through a stack. We conjecture the number of permutations sortable by n – 5 passes, and also the form of a formula for the general case n – k, which involves a polynomial expression.

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References

  1. Knuth D.E.: The Art of Computer Programming. Vol. 1: Fundamental Algorithms. Addison-Wesley Publishing Co., Reading, Mass (1969)

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  2. Steingrímsson, E.: Generalized Permutation Patterns—a Short Survey. In: Linton, S.A., Ruskuc, N., Vatter, V. (eds.) “Permutation Patterns, St Andrews 2007”, LMS Lecture Note Series. Cambridge University Press, Cambridge, to appear

  3. West, J.: Permutations with Forbidden Subsequences; and, Stack Sortable Permutations. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge (1990)

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Authors and Affiliations

  1. The Mathematics Institute, Reyjavík University, 103, Reykjavík, Iceland

    Anders Claesson & Einar Steingrímsson

  2. Science Institute, University of Iceland, 107, Reykjavík, Iceland

    Mark Dukes

Authors
  1. Anders Claesson
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  2. Mark Dukes
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  3. Einar Steingrímsson
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Corresponding author

Correspondence to Anders Claesson.

Additional information

Supported by grant no. 060005013 from the Icelandic Research Fund.

The author acknowledges funding by the EC’s Research Training Network ‘Algebraic Combinatorics in Europe’, grant HPRN-CT-2001-00272 while at Université Bordeaux 1, France.

Supported by grant no. 060005013 from the Icelandic Research Fund.

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Claesson, A., Dukes, M. & Steingrímsson, E. Permutations Sortable by n – 4 Passes Through a Stack. Ann. Comb. 14, 45–51 (2010). https://doi.org/10.1007/s00026-010-0044-7

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  • DOI: https://doi.org/10.1007/s00026-010-0044-7

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