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Moriah and Schultens have demonstrated that an irreducible Heegaard splitting of an orientable Seifert fibered space over an orientable base surface is either vertical or horizontal. In this paper it is determined precisely which vertical and horizontal splittings are irreducible. Let M be a Seifert fibered space which admits a horizontal splitting at the fiber f . If the genus of the horizontal splitting at f is less than the genus of the vertical splittings, its genus will be minimal and thedoi:10.2140/pjm.1999.190.173 fatcat:bsooyt33tbglzo2tqghkk2kvlu