Talha Arıkan, Emrah Kılıç and Toufik Mansour

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 23, 2017, Number 3, Pages 123—132

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## Details

### Authors and affiliations

Talha Arıkan

*Department of Mathematics, Hacettepe University
Ankara, Turkey
*

Emrah Kılıç

*Department of Mathematics, TOBB Economy and Technology University
06560, Ankara, Turkey
*

Toufik Mansour

*Department of Mathematics, University of Haifa
3498838 Haifa, Israel
*

### Abstract

In this paper, we make a contribution to the enumeration of permutations avoiding a quadruples of 4-letter patterns by establishing a Wilf class composed of 19 symmetry classes.

### Keywords

- Pattern avoidance
- Wilf-equivalence

### AMS Classification

- 05A05
- 05A15

### References

- Atkinson, M. D. & Stitt, T. (2002) Restricted permutations and the wreath product, Discrete Math. 259, 19–36.
- Callan, D. & Mansour, T. (2017) A Wilf class composed of 7 symmetry classes of triples of 4-letter patterns, J. Analysis Num. Theory 5:1, 19–26.
- Callan, D. & Mansour, T. (2017) On permutations avoiding 1324, 2143, and another 4-letter pattern, PuMA 26:1, 1–10.
- Callan, D. & Mansour, T. (2017) On permutations avoiding 1243, 2134, and another 4-letter pattern, PuMA 26:1, 11–21.
- Callan, D., Mansour, T. & Shattuck, M. (2017) Wilf classification of triples of 4-letter patterns I, Discrete Math. Theoret. Comput. Sci. 19:1, #5, 35pp.
- Callan, D., Mansour, T. & Shattuck, M. (2017) Wilf classification of triples of 4-letter patterns II, Discrete Math. Theoret. Comput. Sci. 19:1, #6, 44pp.
- Knuth, D. E. (1997) The Art of Computer Programming, 3rd edition, Addison Wesley, Reading, MA.
- Heubach, S. & Mansour, T. (2009) Combinatorics of Compositions and Words, CRC Press, Boca Raton, FL.
- Mansour, T. (2012) Combinatorics of Set Partitions, CRC Press, Boca Raton, FL
- Mansour, T. & Schork, M. (2016) Wilf classification of subsets of four letter patterns, Journal of Combinatorics and Number Theory, 8:1, 1–129.
- Mansour, T. & Schork, M. (2016) Wilf classification of subsets of eight and nine four-letter patterns, Journal of Combinatorics and Number Theory, 8:3, 257–283.
- Simion, R. & Schmidt, F. W. (1985) Restricted permutations, European J. Combin., 6, 383– 406.
- Wilf, H. (1990) Generating functionology, Academic Press, New York.

## Related papers

## Cite this paper

APAArıkan, T., Kılıç, E. & Mansour, T. (2017). A Wilf class composed of 19 symmetry classes of quadruples of 4-letter patterns, Notes on Number Theory and Discrete Mathematics, 23(3), 79-99.

ChicagoArıkan, Talha, Emrah Kılıç, and Toufik Mansour. “A Wilf class composed of 19 symmetry classes of quadruples of 4-letter patterns.” Notes on Number Theory and Discrete Mathematics 23, no. 3 (2017): 179-99.

MLAArıkan, Talha, Emrah Kılıç, and Toufik Mansour. “A Wilf class composed of 19 symmetry classes of quadruples of 4-letter patterns.” Notes on Number Theory and Discrete Mathematics 23.3 (2017): 79-99. Print.