Summary: The Catalan threshold arrangement is a hyperplane arrangement defined by $x_{i} + x_{j} = 0,1,-1$. Using the finite field method, we obtain the number of regions and the characteristic polynomial of the Catalan threshold arrangement. We also give the exponential generating function for the characteristic polynomial of the Catalan threshold arrangement.

52C35, 05A15

hyperplane arrangement, Catalan threshold arrangement, finite field method