Limit shape of perfect matchings on rail-yard graphs

Zhongyang Li

Limit shape of perfect matchings on rail-yard graphs

Combinatorics 2022-04-15 v2 Probability

Authors: Zhongyang Li

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.

Keywords

perfect matchings rail-yard graphs limit shape frozen boundary cloud curve partition boundary conditions

Cite

@article{arxiv.2110.11351,
  title  = {Limit shape of perfect matchings on rail-yard graphs},
  author = {Zhongyang Li},
  journal= {arXiv preprint arXiv:2110.11351},
  year   = {2022}
}