English

From Dominoes to Hexagons

Combinatorics 2016-09-13 v2 Geometric Topology Quantum Algebra

Abstract

There is a natural generalization of domino tilings to tilings of a polygon by hexagons, or, dually, configurations of oriented curves that meet in triples. We show exactly when two such tilings can be connected by a series of moves analogous to the domino flip move. The triple diagrams that result have connections to Legendrian knots, cluster algebras, and planar algebras.

Keywords

Cite

@article{arxiv.math/0405482,
  title  = {From Dominoes to Hexagons},
  author = {Dylan P. Thurston},
  journal= {arXiv preprint arXiv:math/0405482},
  year   = {2016}
}

Comments

17 pages, 5 figures; v2: clarified proofs and conjectures