Freeness of a hyperplane arrangement is defined algebraically
using module of derivations. And it has an interesting combinatorial
property: Terao's factorization theorem for characteristic polynomial.
I will talk about the freeness of extended Catalan/Shi arrangements
and its combinatorial corollaries.
In the proof, I will discuss a characterization for freeness.
And a possible relation between algebraic properties of the derivation
module and combinatorics of characteristic polynomial, such as
``positions of zeros'', will also be discussed.