Journal of Combinatorics
Volume 9 (2018)
Inverting the rational sweep map
Pages: 659 – 679
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