  In an earlier paper, we introduced ``bordered knot algebras'', which
  are graded algebras indexed by a pair of integers (m,k). In a
  subsequent paper, we introduced a two-parameter family of
  differential graded algebra, the ``pong algebras'', and identified
  their homology with the bordered knot algebras, and characterized
  the induced A-infinity structure on the homology. The aim of the
  present paper is to give an explicit, combinatorial model for this
  A-infinity structure on the bordered knot algebras, and a further
  weighted deformation of this structure, in the case where k=1.
