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In their 2002 paper, Ciucu and Krattenthaler proved several product formulasfor the number of lozenge tilings of various regions obtained from a centrallysymmetric hexagon on the triangular lattice by removing maximal staircaseregions from two non-adjacent corners. For the case when the staircases areremoved from adjacent corners of the hexagon, they presented two conjecturalformulas, whose proofs, as they remarked, seemed at the time "a formidabletask". In this paper we prove those two conjectures. Our proofs proceed byfirst generalizing the conjectures, and then proving them by induction, usingKuo's graphical condensation method.

Proof of two conjectures of Ciucu and Krattenthaler on the enumeration of lozenge tilings of hexagons with cut off corners