  In the seminal work of Stanley, several conjectures were made on the
structure of Littlewood-Richardson coefficients for the multiplication of Jack
symmetric functions. Motivated by recent results of Alexandersson and the
present author, we postulate that a certain 'windowing' property holds for all
such Jack L-R coefficients. This property provides a vast set of relations
between these coefficients and allows for their direct computation in certain
novel cases. We demonstrate compatibility between our windowing conjecture and
the conjectures of Stanley, with the hope of illuminating the structures
within.
