  We prove that the HOMFLYPT polynomial of a link, colored by partitions with a
fixed number of rows is a $q$-holonomic function. Specializing to the case of
knots colored by a partition with a single row, it proves the existence of an
$(a,q)$ super-polynomial of knots in 3-space, as was conjectured by string
theorists. Our proof uses skew Howe duality that reduces the evaluation of web
diagrams and their ladders to a Poincare-Birkhoff-Witt computation of an
auxiliary quantum group of rank the number of strings of the ladder diagram.
