Link degree distribution, symmetrized Hasse diagram Laplacian eigenvalues, and causal interval abundance distinguish nine classes of causal sets.
A guide to mathematical quasicrystals
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abstract
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular, we focus on their interplay with various physically motivated equivalence concepts such as local indistinguishability and local equivalence. Various discrete patterns with non-crystallographic symmetries are described in detail, and some of their magic properties are introduced. This perfectly ordered world is augmented by a brief introduction to the stochastic world of random tilings.
fields
gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Charting causal set configuration space with graph observables
Link degree distribution, symmetrized Hasse diagram Laplacian eigenvalues, and causal interval abundance distinguish nine classes of causal sets.