Toufik Mansour and Mark Shattuck

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

Volume 20, 2014, Number 2, Pages 74—78

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## Details

### Authors and affiliations

Toufik Mansour

*Department of Mathematics, University of Haifa
31905 Haifa, Israel*

Mark Shattuck

*Department of Mathematics, University of Haifa
31905 Haifa, Israel*

### Abstract

Dokos et al. recently conjectured that the distribution polynomial *f _{n}*(

*q*) on the set of permutations of size

*n*avoiding the pattern 321 for the number of inversions is given by:

with

*f*

_{0}(

*q*) = 1, which was later proven in the affirmative, see [1]. In this note, we provide a new proof of this conjecture, based on the scanning-elements algorithm described in [3], and present an identity obtained by equating two explicit formulas for the generating function .

### Keywords

- Avoidance
- Inversion number
- q-analogue
- Continued fractions
- Permutations

### AMS Classification

- 11B37
- 11B65
- 05A15

### References

- Cheng, S.-E., S. Elizalde, A. Kasraoui, B. E. Sagan. Inversion and major index polynomials, Preprint, http://arxiv.org/pdf/1112.6014.pdf.
- Dokos, T., T. Dwyer, B. P. Johnson, B. E. Sagan, K. Selsor. Permutation patterns and statistics, Discrete Math., Vol. 312, 2012, 2760–2775.
- Firro, G., T. Mansour. Three-letter-pattern-avoiding permutations and functional equations, Electron. J. Combin., Vol. 13, 2006, #R51.
- Fürlinger, J., J. Hofbauer, q-Catalan numbers, J. Combin. Theory Ser. A, Vol. 40, 1985, No. 2, 248–264.

## Related papers

## Cite this paper

APAMansour, T. & Shattuck, M. (2014). On a recurrence related to 321-avoiding permutations. Notes on Number Theory and Discrete Mathematics, 20(2), 74-78.

ChicagoMansour, Toufik, and Mark Shattuck. “On a Recurrence Related to 321-Avoiding Permutations.” Notes on Number Theory and Discrete Mathematics 20, no. 2 (2014): 74-78.

MLAMansour, Toufik, and Mark Shattuck. “On a Recurrence Related to 321-Avoiding Permutations.” Notes on Number Theory and Discrete Mathematics 20.2 (2014): 74-78. Print.