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Results tagged with reference-request
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user 143153
This tag is used if a reference is needed in a paper or textbook on a specific result.
4
votes
2
answers
270
views
Lower bounds for pattern complexity of aperiodic subshifts
In the setting of symbolic dynamics over $\mathbb{Z}^d$, one can define for the $n$-th pattern complexity of a given a subshift $\Omega\subseteq \mathcal{A}^{\mathbb{Z}^d}$ as
$$ c_n(\Omega):= \Big\ve …
- 633
1
vote
1
answer
145
views
Approximation of subshifts in Hausdorff distance
I have recently been interested in some questions which stem from taking subshifts which converge to a limiting subshift in the Hausdorff metric.
More specifically, given an alphabet $\mathcal{A}$, I …
- 633
1
vote
1
answer
146
views
Properties of limit set for cellular automata
Is anyone familiar with results about properties of the limit set of the local rule for a cellular automaton? I haven't been able to find any good materials on the subject from an initial search, and …
- 633
0
votes
1
answer
68
views
Computing spectrum of very simple Schrödinger operator
I asked this question recently on a thread in math stack exchange, but with no real answers suggested. I think this is a relatively simple variation on the classical free Laplacian spectrum, so I assu …
- 633
1
vote
0
answers
87
views
Measure estimates of $\delta$-neighbourhood of compact sets
I am interested in the estimating from above the measure of a compact set $K$ by a sequence of sets $K_n$, converging to it in the Hausdorff metric. As such I am looking for known conditions that give …
- 633
1
vote
2
answers
98
views
A variation of domino tiling problem with fusions
I know several specific variations of the domino tiling problem has been determined to be decidable or undecidable, such as the seed domino problem. I have a variation which I have not been able to f …
- 633
3
votes
0
answers
58
views
Maximal number of aperiodic Wang tiles
I was wondering whether there is an analogue result to the minimality of Wang tiling, in the direction of maximality.
I think that the paper by Jeandel and Rao, shows that the minimal number of Wang t …
- 633
2
votes
1
answer
127
views
Reference on relation between SFTs and Wang-tiles
I've been looking at several papers which allude to a relation between SFTs. Namely, given an SFT $\Omega \subseteq \mathcal{A}^{\mathbb{Z}^2}$ with allowed patches $\mathcal{F}$, we can associate a s …
- 633
3
votes
1
answer
87
views
Asymptotic growth rate for primitve S-adic systems
It is known that for a primitive substitution $S:\mathcal{A}\to \mathcal{A}^+$, there exists constants $c,C>0$ such that
$$ c\theta_S^n \leq \vert S^n(a)\vert \leq C \theta_S^n \quad \text{for all} \; …
- 633
0
votes
0
answers
60
views
Recognizability of a substitution implies aperiodicity
Is there a good reference, aside from the book of "Tilings and Patterns" by Grunbaum and Shephard, on the fact that recognizability\unique-composition of a tiling implies aperiodicity? I unfortunately …
- 633