Dinv and Area

Adriano Garsia, Guoce Xin


We give a new combinatorial proof of the well known result that the dinv of an $(m,n)$-Dyck path is equal to the area of its sweep map image. The first proof of this remarkable identity for co-prime $(m,n)$ is due to Loehr and Warrington. There is also a second proof (in the co-prime case) due to Gorsky and Mazin and a third proof due to Mazin.


A corrigendum was added to this paper on the 9th of June 2017.


Rational Dyck paths; Sweep map; Dinv

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