Dinv and Area
Copyright policy )Dinv and Area
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.
- Capital Normal University China (People's Republic of)
- University of California, San Diego United States
Combinatorial aspects of partitions of integers, Exact enumeration problems, generating functions, dinv, FOS: Mathematics, rational Dyck paths, Mathematics - Combinatorics, sweep map, Combinatorics (math.CO), 05E99
Combinatorial aspects of partitions of integers, Exact enumeration problems, generating functions, dinv, FOS: Mathematics, rational Dyck paths, Mathematics - Combinatorics, sweep map, Combinatorics (math.CO), 05E99
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