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In this paper we study the relation between pyramid partitions with a generalempty room configuration (ERC) and the BPS states of D-branes on the resolvedconifold. We find that the generating function for pyramid partitions with alength n ERC is exactly the same as the D6/D2/D0 BPS partition function on theresolved conifold in particular Kaehler chambers. We define a new type ofpyramid partition with a finite ERC that counts the BPS degeneracies in certainother chambers.  The D6/D2/D0 partition functions in different chambers were obtained byapplying the wall crossing formula. On the other hand, the pyramid partitionsdescribe T^3 fixed points of the moduli space of a quiver quantum mechanics.This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system onthe conifold and choose a particular set of FI parameters. The arrow structureof the dual quiver is confirmed by computation of the Ext group between thesheaves. We show that the superpotential and the stability condition of thedual quiver with this choice of the FI parameters give rise to the rulesspecifying pyramid partitions with length n ERC.

Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions