Inversion polynomials for 321-avoiding permutations

@article{Cheng2013InversionPF,
  title={Inversion polynomials for 321-avoiding permutations},
  author={Szu-En Cheng and Sergi Elizalde and Anisse Kasraoui and Bruce E. Sagan},
  journal={Discrete Mathematics},
  year={2013},
  volume={313},
  pages={2552-2565}
}
We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin paths, polyominoes, and continued fractions. 

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