Determinant formulas for the $\tau$-functions of the Painlev\'e   equations of type $A$
  Explicit determinant formulas are presented for the $\tau$ functions of the generalized Painlev\'e equations of type $A$. This result allows an interpretation of the $\tau$-functions as the Pl\"ucker coordinates of the universal Grassmann manifold. 
Yasuhiko Yamada