  We present multiresidue formulae for partial sums in the basis of link
patterns of the polynomial solution to the level 1 U_q(\hat sl_2) quantum
Knizhnik--Zamolodchikov equation at generic values of the quantum parameter q.
These allow for rewriting and generalizing a recent conjecture [Di Francesco
'06] connecting the above to generating polynomials for weighted Totally
Symmetric Self-Complementary Plane Partitions. We reduce the corresponding
conjectures to a single integral identity, yet to be proved.
