Catalan numbers, parking functions, permutahedra and noncommutative Hilbert schemes

Valery Lunts, Špela Špenko, Michel Van den Bergh

We find an explicit $S_n$-equivariant bijection between the integral points in a certain zonotope in ${\mathbb{R}}^n$, combinatorially equivalent to the permutahedron, and the set of…