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

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In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold.

• We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kaehler chambers.
• We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers.
• The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula.