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.
@article{10_37236_6501,
author = {Adriano Garsia and Guoce Xin},
title = {Dinv and area},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6501},
zbl = {1358.05022},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6501/}
}
TY - JOUR
AU - Adriano Garsia
AU - Guoce Xin
TI - Dinv and area
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6501/
DO - 10.37236/6501
ID - 10_37236_6501
ER -
%0 Journal Article
%A Adriano Garsia
%A Guoce Xin
%T Dinv and area
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6501/
%R 10.37236/6501
%F 10_37236_6501
Adriano Garsia; Guoce Xin. Dinv and area. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6501
