On uniformly generating Latin squares

Details On uniformly generating Latin squares On uniformly generating Latin squares

2010-05-02

arxiv.org/abs/1005.0121v2

Mathematics

Combinatorics

14 pages; The version to be published in Bull. Inst. Combin. Appl.

Scientific paper

By simulating an ergodic Markov chain whose stationary distribution is uniform over the space of nxn Latin squares, Mark T. Jacobson and Peter Matthews [4], have discussed elegant methods by which they generate Latin squares with a uniform distribution (approximately). The central issue is the construction of "moves" that connect the squares. Most of their lengthy paper is to prove that the associated graph is indeed connected. We give a short proof of this fact by using the concepts of Latin bitrades.

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