English

Dinv and Area

Combinatorics 2017-05-24 v2

Abstract

We give a new combinatorial proof of the well known result that the dinv of an (m,n)(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)(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.

Cite

@article{arxiv.1609.04480,
  title  = {Dinv and Area},
  author = {Adriano M. Garsia and Guoce Xin},
  journal= {arXiv preprint arXiv:1609.04480},
  year   = {2017}
}

Comments

9 pages, 6 figures

R2 v1 2026-06-22T15:50:14.589Z