Enumeration of perfect matchings in graphs with reflective symmetry
Journal of Combinatorial Theory Series A
Strip tiling and regular grammars
Theoretical Computer Science
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Theoretical Computer Science
Enumerating tatami mat arrangements of square grids
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Monomer-dimer tatami tilings of square regions
Journal of Discrete Algorithms
Hi-index | 5.23 |
This paper continues the investigation of tiling problems via formal languages, which was begun in papers by Merlini, Sprugnoli, and Verri. Those authors showed that certain tiling problems could be encoded by regular languages, which lead automatically to generating functions and other combinatorial information on tilings. We introduce a method of simplifying the DFA's recognizing these language, which leads to bijective proofs of certain tiling identities. We apply these ideas to some other tiling problems, including three-dimensional tilings and tilings with triangles and rhombi. We also study graph-theoretic variations of these tiling problems.