What to find on this page
Here you can find my research projects in Mathematics.
A comprehensive list of the articles I am working in:
- A.S., M. D'Adderio - A rational Loehr-Remmel bijection and Sorted sandpiles (still working on a publishable version...)
- A.S., M. D'Adderio - A new look into the Loehr-Remmel bijection (still working on a publishable version...)
On the side menu you can find an abstract version of the papers listed above.
What to find on this page
Here you can find my research projects in Mathematics.
A comprehensive list of the articles I am working in:
- A.S., M. D'Adderio - A rational Loehr-Remmel bijection and Sorted sandpiles (still working on a publishable version...)
- A.S., M. D'Adderio - A new look into the Loehr-Remmel bijection (still working on a publishable version...)
On the side menu you can find an abstract version of the papers listed above.
A.S., M. D'Adderio - A new look into the Loehr-Remmel bijection
Abstract
The objective of this paper is to give a more intuitive interpretation to the Loehr-Remmel bijection.
More specifically, we try to give an explicit construction of the inverse map, which previously has only been described undirectly through intermediate classes of combinatorial objects.
A.S., M. D'Adderio - A rational Loehr-Remmel bijection and Sorted sandpiles
Abstract
We introduce a generalized $\text{pmaj}$ statistic for $(nk,n)$-parking functions and prove the Loehr-Remmel bijection in this rational case.
This combinatorial class can also be interpreted in the Sorted Sandpile model with a new family of underlying graphs and bi-statistic $(\text{level},\text{delay})$.
With these objects we obtain two new formulation of the $(nk,n)$-Rational Shuffle Theorem.