Journal of Combinatorics

Volume 9 (2018)

Number 4

Inverting the rational sweep map

Pages: 659 – 679



Adriano Garsia (Department of Mathematics, University of California at San Diego)

Guoce Xin (School of Mathematical Sciences, Capital Normal University, Beijing, China)


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.


rational Dyck paths, sweep maps, path diagrams

2010 Mathematics Subject Classification

05A19, 05A99, 05E05

Adriano Garsia was supported by NFS grant DMS13–62160.

Guoce Xin was supported by National Natural Science Foundation of China (11171231).

Received 20 March 2016

Published 7 December 2018