Abstract
AbstractWe 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 one 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.
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