Exact solution to the quantum and classical dimer models on the spectre aperiodic monotiling
The decades-long search for a shape that tiles the plane only aperiodically under
translations and rotations recently ended with the discovery of the “spectre” aperiodic …
translations and rotations recently ended with the discovery of the “spectre” aperiodic …
Compression theory for inhomogeneous systems
The physics of complex systems stands to greatly benefit from the qualitative changes in
data availability and advances in data-driven computational methods. Many of these …
data availability and advances in data-driven computational methods. Many of these …
Hexagonal quasiperiodic tilings as decorations of periodic lattices
S Coates - arXiv preprint arXiv:2404.11378, 2024 - arxiv.org
Symmetry sharing facilitates coherent interfaces which can transition from periodic to
quasiperiodic structures. Motivated by the design and construction of such systems, we …
quasiperiodic structures. Motivated by the design and construction of such systems, we …
Metallic mean fractal systems and their tilings
S Coates - arXiv preprint arXiv:2405.04458, 2024 - arxiv.org
Fractals and quasiperiodic structures share self-similarity as a structural property. Motivated
by the link between Fibonacci fractals and quasicrystals which are scaled by the golden …
by the link between Fibonacci fractals and quasicrystals which are scaled by the golden …
Average Degree of Graphs Derived From Aperiodic Tilings
X Xu, DC Ong - arXiv preprint arXiv:2408.07707, 2024 - arxiv.org
We consider graphs derived from aperiodically ordered tilings of the plane, by treating each
corner of each tile as a vertex and each side of each tile as an edge. We calculate the …
corner of each tile as a vertex and each side of each tile as an edge. We calculate the …
[PDF][PDF] The structure of the 2-factor transfer digraph common for thin cylinder, torus and Klein bottle grid graphs
KD Jelena-Dokica, O Bodroza-Panticb - Filomat, 2024 - pmf.ni.ac.rs
We prove that the transfer digraph D∗ C, m needed for the enumeration of 2-factors in the
thin cylinder TnCm (n), torus TGm (n) and Klein bottle KBm (n)(all grid graphs of the fixed …
thin cylinder TnCm (n), torus TGm (n) and Klein bottle KBm (n)(all grid graphs of the fixed …
[PDF][PDF] Tree-width, Walk-width, circuit-width, wheel-width, grid-width, cubic-width, and regular-width
T Fujita - researchgate.net
In this paper, we explore various graph structures and introduce width parameters to
measure how closely a graph approximates these structures. We define and analyze tree …
measure how closely a graph approximates these structures. We define and analyze tree …