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The method of topological vertex for topological string theory on toricCalabi-Yau 3-folds is reviewed. Implications of an explicit formula ofpartition functions in the "on-strip" case, typically the generalizedconifolds, are considered. Generating functions of part of the partitionfunctions are shown to be tau functions of the KP hierarchy. The associatedBaker-Akhiezer functions play the role of wave functions, and satisfy$q$-difference equations. These $q$-difference equations represent the quantummirror curves conjectured by Gukov and Su{\l}kowski.

Remarks on partition functions of topological string theory on generalized conifolds