On the conjecture of Athanasiadis related to freeness of a family of   hyparplane arrangements
  We prove a characterization of freeness, conjectured by Athanasiadis, for the family of hyperplane arrangements which lie between the Coxeter and the Catalan arrangement of type $A_\ell$. One direction was already proved in [2]. Here we prove the other direction 
Takuro Abe
math.CO math.AC