Parking functions, Shi arrangements, and mixed graphs

Matthias Beck, Ana Berrizbeitia, Michael Dairyko +3

The \emph{Shi arrangement} is the set of all hyperplanes in ${\mathbb{R}}^n$ of the form $x_j-x_k=0$ or $1$ for $1\le j<k\le n$. Shi observed in 1986 that the number of region…