A note on domino shuffling

Élise Janvresse (1) , Thierry de La Rue (1) , Yvan Velenik (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We present a variation of James Propp's generalized domino shuffling, which provides an efficient way to obtain perfect matchings of weighted Aztec diamonds. Our modification is specially tailored to deal with cases when some of the weights are zero. This allows us to tile efficiently a large class of planar graphs, by embedding them in a large enough Aztec diamond. We also give a sufficient condition on the size of the latter diamond for the algorithm to succeed.

Mots clés: Domino shuffling; Perfect matching; Random tiling; Random generation; Aztec Diamond

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Élise Janvresse, Thierry de La Rue, Yvan Velenik. A note on domino shuffling. The Electronic Journal of Combinatorics, 2006, 13 (1), pp.R30. ⟨hal-00007996v3⟩