  This paper calculates the number of full exceptional collections modulo an
action of a free abelian group of rank one for an abelian category of coherent
sheaves on an orbifold projective line with a positive orbifold Euler
characteristic, which is equivalent to the one of finite dimensional modules
over an extended Dynkin quiver of ADE type by taking their derived categories.
This is done by a recursive formula naturally generalizing the one for the
Dynkin case by Deligne whose categorical interpretation is due to
Obaid--Nauman--Shammakh--Fakieh--Ringel.
  Moreover, the number coincides with the degree of the Lyashko--Looijenga map
of the Frobenius manifold for the orbifold projective line, which hints a
consistency in some problems in Bridgeland's stability conditions and mirror
symmetry.
