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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## Details

### 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
*

### Abstract

Let 𝑆_{𝑛} 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.

### Keywords

- Pattern avoidance
- Wilf-equivalence

### 2010 Mathematics Subject Classification

- 05A15
- 05A05

### References

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- Mansour, T. & Schork, M. (2018) Permutation patterns and cell decompositions, Mathematics in Computer Science, to appear, https://doi.org/10.1007/s11786-018-0353-5.
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- Vatter, V. (2012) Finding regular insertion encodings for permutation classes, Journal of Symbolic Computation, 47(3), 259–265.

## Related papers

## Cite this paper

APACallan, 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.

ChicagoCallan, David, and Toufik Mansour. “Enumeration of 3- and 4-Wilf Classes of Four 4-letter Patterns.” Notes on Number Theory and Discrete Mathematics 24, no. 3 (2018): 115-130, doi: 10.7546/nntdm.2018.24.3.115-130.

MLACallan, David, and Toufik Mansour. “Enumeration of 3- and 4-Wilf Classes of Four 4-letter Patterns.” Notes on Number Theory and Discrete Mathematics 24.3 (2018): 115-130. Print, doi: 10.7546/nntdm.2018.24.3.115-130.