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This paper calculates the number of full exceptional collections modulo anaction of a group as the set generated by spherical twists for an abeliancategory of coherent sheaves on an orbifold projective line with a zeroorbifold Euler characteristic. This is done by a recursive formula naturallygeneralizing the one for the Dynkin case by Deligne whose categoricalinterpretation is due to Obaid-Nauman-Shammakh-Fakieh-Ringel and an abeliancategory of coherent sheaves on an orbifold projective line with a positiveorbifold Euler characteristic is due to Otani-Shiraishi-Takahashi.

Number of full exceptional collections modulo spherical twists for elliptic orbifolds