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