Inversion polynomials for 321-avoiding permutations
Combinatorics
2012-11-21 v3
Abstract
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.
Cite
@article{arxiv.1112.6014,
title = {Inversion polynomials for 321-avoiding permutations},
author = {Szu-En Cheng and Sergi Elizalde and Anisse Kasraoui and Bruce Sagan},
journal= {arXiv preprint arXiv:1112.6014},
year = {2012}
}
Comments
This new version is in its final state with added exposition, examples, and results