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Results tagged with co.combinatorics
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user 143153
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
1
answer
192
views
'Trivial' lower bounds for pattern complexity of aperiodic subshifts
I recently asked in this thread about lower bounds on the complexity in the case where we have an aperiodic subshift. If I denote $c_n(\Omega)$ as the number of possible patterns on $Q_n= \big\{ 0,... …
- 633
1
vote
2
answers
325
views
Sufficient conditions for periodic tiling by Wang tiles
I'm recently interested in whether a sub-shift of finite type contains a doubly-periodic problem, when the set of configurations is of the sort $\mathcal{A}^{\mathbb{Z}^2}$. When $Q_2=\{0,1\}^2$, and …
- 633
0
votes
Sufficient conditions for periodic tiling by Wang tiles
I believe I have found some nontrivial conditions from two papers.
First, if the number of colors used in the Wang tiles is strictly less than $4$, the Wang tiles must allow a periodic tiling. This re …
- 633
0
votes
Recognizability/unique composition property for substitution tiling
Following Ville Salo's comments I came across upon Pansiot's paper, DECIDABILITY OF PERIODICITY FOR INFINITE WORDS. The papers shows an algorithm to decide whether an infinite word fixed by a substitu …
- 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
1
vote
1
answer
128
views
Recognizability/unique composition property for substitution tiling
This may be a very basic question, but I have not found an answer to it so far in my search. The question is whether there is an "algorithmic" way to check unique-composition/recognizability of a tili …
- 633