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Phase Transitions in Random Dyadic Tilings and Rectangular Dissections

2018
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SIAM Journal on Discrete Mathematics
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We study rectangular dissections of an n × n lattice region into rectangles of area n, where n = 2 k for an even integer k. We show that there is a natural edgeflipping Markov chain that connects the state space. A similar edge-flipping chain is also known to connect the state space when restricted to dyadic tilings, where each rectangle is required to have the form where s, t, u and v are nonnegative integers. The mixing time of these chains is open. We consider a weighted version of these

doi:10.1137/17m1157118
fatcat:trdh4oa6vren3j4c6xzgcxlicq