
TL;DR
This paper provides a new combinatorial proof of the identity linking dinv and area for (m,n)-Dyck paths, expanding understanding of these combinatorial objects and their properties.
Contribution
It introduces a novel combinatorial proof of the dinv-area equality for (m,n)-Dyck paths, complementing existing proofs.
Findings
New combinatorial proof of dinv equals area for (m,n)-Dyck paths
Extends understanding of Dyck path statistics
Supports existing identities with an alternative approach
Abstract
We give a new combinatorial proof of the well known result that the dinv of an -Dyck path is equal to the area of its sweep map image. The first proof of this remarkable identity for co-prime 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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology
