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math.CO2026
A Loehr-Remmel bijection in the grid and sandpiles
Michele D'Adderio, Alessio Sgubin
We extend the statistic of Loehr and Remmel to labelled Dyck paths in the grid, and generalize their bijection sending the bistatistic $(\mathsf{dinv}…
math.CO2026
Leaving the Hall: explicit formulas for Negut operators
Michele D'Adderio, Giovanni Interdonato, Alessandro Iraci +1
Recent major breakthroughs in -combinatorics include the introduction of the Dyck path algebra by Carlsson and Mellit and of the Catalanimals by Blasiak et…
math.CO2026
On a bijection of Loehr and Remmel
Michele D'Adderio, Alessio Sgubin
In this expository article we review a remarkable bijection due to Loehr and Remmel from the set of parking functions of size n into itself, which sends the bistatistic (dinv…