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

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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