Can I read On the Sweep Map for $\vec{k}$-Dyck Paths on EtoBox?

On the Sweep Map for $\vec{k}$-Dyck Paths by Xin, Guoce; Zhang, Yingrui is a scholarly article available to read on EtoBox.

What is On the Sweep Map for $\vec{k}$-Dyck Paths about?

Garsia and Xin gave a linear algorithm for inverting the sweep map for Fuss rational Dyck paths in $D_{m,n}$ where $m=kn\pm 1$. They introduced an intermediate family $\mathcal{T}_n^k$ of certain standard Young tableau. Then inverting the sweep map is done by a simple walking algorithm on a $T\in \mathcal{T}_n^k$. We find their idea naturally extends for $\mathbf{k}^\pm$-Dyck paths, and also for $\mathbf{k}$-Dyck paths (reducing to $k$-Dyck paths for the equal parameter case). The intermediate object becomes a similar type of tableau in $\mathcal{T}_\mathbf{k}$ of different column lengths. This approach is independent of the Thomas-Williams algorithm for inverting the general modular sweep map.

Author

Xin, Guoce; Zhang, Yingrui

Published

2018

Language

EN