  We obtain a new formula to relate the value of a Schur polynomial with
variables $(x_1,\ldots,x_N)$ with values of Schur polynomials at
$(1,\ldots,1)$. This allows to study the limit shape of perfect matchings on a
square hexagon lattice with periodic weights and piecewise boundary conditions.
In particular, when the edge weights satisfy certain conditions, asymptotics of
the Schur function imply that the liquid region of the model in the scaling
limit has multiple connected components, while the frozen boundary consists of
disjoint cloud curves.
