A. Garsia

activity

20002022

most citedCompositional (km,kn)-Shuffle Conjectures

20 citations · 64 across the 20 of their papers we have counts for

collaborators

Showing 2016Show all

3 papers · 1 filter

math.CO2016

Dinv and Area

Adriano M. 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 ide…

math.CO2016

Five-term relation and Macdonald polynomials

Adriano Garsia, Anton Mellit

The non-commutative five-term relation $T_{1, 0} T_{0, 1} = T_{0, 1} T_{1, 1} T_{1, 0}$ is shown to hold for certain operators acting on symmetric functions. The "generalized recursion"…

math.CO2016★ 2 cited

Inverting the Rational Sweep Map

Adriano M. Garsia, Guoce Xin

We present a simple algorithm for inverting the sweep map on rational $(m, n)$ -Dyck paths for a co-prime pair $(m, n)$ of positive integers. This work is inspired by Thomas-Williams…