Inverting the Rational Sweep Map
  We present a simple algorithm for inverting the sweep map on rational $(m,n)$-Dyck paths for a co-prime pair $(m,n)$ of positive integers. This work is inspired by Thomas-Williams work on the modular sweep map. A simple proof of the validity of our algorithm is included. 
Adriano M. Garsia and Guoce Xin
math.CO