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arXiv · 2110.11351

Limit shape of perfect matchings on rail-yard graphs

Zhongyang Li
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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.

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Zhongyang Li. 2022-04-14. Limit shape of perfect matchings on rail-yard graphs. https://arxiv.org/abs/2110.11351

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