ETD

• algebra of diagonal coinvariants
• combinatorics
• Loehr-Remmel bijection
• parking functions
• sandpiles
• shuffle conjecture
• sorted sandpiles

In this work, we introduce a generalized pmaj statistic for (n,nk)-parking functions. We provide a new construction for the classical Loehr-Remmel bijection and prove a generalized bijection in the rational (n,nk) case.

This combinatorial class can also be interpreted in the Sorted Sandpile model with a new family of underlying graphs and bi-statistic (level,delay).

With these objects we obtain two new formulation of the (n,nk)-Rational Shuffle Theorem.