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Limit shape of perfect matchings on rail-yard graphs (2110.11351v2)
Published 21 Oct 2021 in math.CO and math.PR
Abstract: We obtain limit shape of perfect matchings on a large class of rail-yard graphs with right boundary condition given by the empty partition, and left boundary condition given by either by a staircase partition with constant density or a piecewise partition with densities either 1 or 0. We prove the parametric equations for the frozen boundary, and find conditions under which the frozen boundary is a cloud curve, or a union of disjoint cloud curves.