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We verify a recent conjecture of Kenyon/Szendroi, arXiv:0705.3419, bycomputing the generating function for pyramid partitions. Pyramid partitionsare closely related to Aztec Diamonds; their generating function turns out tobe the partition function for the Donaldson--Thomas theory of a non-commutativeresolution of the conifold singularity {x1x2 -x3x4 = 0}. The proof does notrequire algebraic geometry; it uses a modified version of the domino shufflingalgorithm of Elkies, Kuperberg, Larsen and Propp.

Computing a pyramid partition generating function with dimer shuffling