Lozenge tilings (rhombus tiling)

introduction

• plane partitions, lozenge tilings of a hexagon, perfect matchings on a honeycomb graph, and families of non-intersecting lattice paths in a hexagon are all in bijection

memo

• http://www.h-k.fr/seb/these/articles/generation_fin_JDA04_Seb.pdf
• rhombus tilings of an abc-hexagon
• http://www.flickr.com/photos/syngola/sets/72157603497791228/
• http://www.citycarshare.org/
• http://icerm.brown.edu/

articles

• Cook II, David, and Uwe Nagel. ‘Signed Lozenge Tilings’. arXiv:1507.02507 [math], 6 July 2015. http://arxiv.org/abs/1507.02507.
• Petrov, Leonid. “Asymptotics of Uniformly Random Lozenge Tilings of Polygons. Gaussian Free Field.” The Annals of Probability 43, no. 1 (February 2015): 1–43. doi:10.1214/12-AOP823.
• Ciucu, Mihai, and Ilse Fischer. “Lozenge Tilings of Hexagons with Arbitrary Dents.” arXiv:1412.3945 [math], December 12, 2014. http://arxiv.org/abs/1412.3945.