Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns

@article{Claesson2012UpperBF,
  title={Upper bounds for the Stanley-Wilf limit of 1324 and other layered patterns},
  author={A. Claesson and V. Jel{\'i}nek and E. Steingr{\'i}msson},
  journal={J. Comb. Theory, Ser. A},
  year={2012},
  volume={119},
  pages={1680-1691}
}
  • A. Claesson, V. Jelínek, E. Steingrímsson
  • Published 2012
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • We prove that the Stanley-Wilf limit of any layered permutation pattern of length ? is at most 4?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… CONTINUE READING

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