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.