Enumeration of 3- and 4-Wilf classes of four 4-letter patterns

David Callan and Toufik Mansour
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 3, Pages 115—130
DOI: 10.7546/nntdm.2018.24.3.115-130
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Authors and affiliations

David Callan
Department of Statistics, University of Wisconsin
Madison, WI 53706, United States

Toufik Mansour
Department of Mathematics, University of Haifa
3498838 Haifa, Israel


Let 𝑆𝑛 be the symmetric group of all permutations of 𝑛 letters. We show that there are precisely 27 (respectively, 15) Wilf classes consisting of exactly 3 (respectively, 4) symmetry classes of subsets of four 4-letter patterns.


  • Pattern avoidance
  • Wilf-equivalence

2010 Mathematics Subject Classification

  • 05A15
  • 05A05


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Cite this paper

Callan, D., & Mansour, T. (2018). Enumeration of 3- and 4-Wilf classes of four 4-letter patterns. Notes on Number Theory and Discrete Mathematics, 24(3), 115-130, doi: 10.7546/nntdm.2018.24.3.115-130.

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