Book contents
- Frontmatter
- Contents
- Preface
- Phase Transitions in Random Planar Graphs
- Extremal Poset Theory
- Techniques for Taming Temporal Graphs
- Asymptotic Enumeration via Graph Containers and Entropy
- Graph Bootstrap Percolation – A Discovery of Slowness
- Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach
- Monadic Second-Order Logic for Hypergraphs and Matroids
- Domino Tilings Beyond 2D
- References
Domino Tilings Beyond 2D
Published online by Cambridge University Press: 06 June 2026
Book contents
- Frontmatter
- Contents
- Preface
- Phase Transitions in Random Planar Graphs
- Extremal Poset Theory
- Techniques for Taming Temporal Graphs
- Asymptotic Enumeration via Graph Containers and Entropy
- Graph Bootstrap Percolation – A Discovery of Slowness
- Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach
- Monadic Second-Order Logic for Hypergraphs and Matroids
- Domino Tilings Beyond 2D
- References
Summary
There is a rich history of domino tilings in two dimensions. Through a variety of techniques, we can answer questions such as: how many tilings are there of a given region, or what does the space of all tilings look like? These questions and their answers become significantly more difficult in dimension three and above. Despite this curse of dimensionality, there have been exciting recent advances in the theory. Here we briefly review foundational results of two-dimensional domino tilings and highlight where challenges arise when generalizing to higher dimensions. We then survey results in higher dimensional domino tilings, focusing on the question of connectivity of the space of tilings, and the open problems that still remain.
Information
- Type
- Chapter
- Information
- Surveys in Combinatorics 2026 , pp. 267 - 292Publisher: Cambridge University PressPrint publication year: 2026
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