Timeline for Mixing coded systems and period of their graph presentations
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 29, 2014 at 7:59 | answer | added | M. Dabbaghian | timeline score: 3 | |
| Apr 6, 2014 at 7:04 | answer | added | user49227 | timeline score: 0 | |
| Mar 31, 2014 at 8:13 | comment | added | Dominik Kwietniak | Usually yes. If there are two generators with relatively prime lengths, then after adding any block the system would still be mixing. | |
| Mar 27, 2014 at 18:54 | comment | added | user39115 | What does happen when you have a mixing coded system $X$ with generators $(w_n)_{n\in\mathbb{N}}$ and you add a new block w, i.e. you consider $X'$ that corresponds to the closure of the sets of sequences obtained by freely concatenating words in $(w_n)_{n\in\mathbb{N}}$ and $w$ ? Is the mixing property preserved? | |
| Feb 9, 2014 at 23:27 | comment | added | Dominik Kwietniak | An equivalent charcterization of coded systems says that a shift space $X$ is a coded system if there exist a countable collection of finite words (blocks) $(w_n)_{n\in\mathbb{N}}$, called generators, such that $X$ is the closure of the set of sequences obtained by freely concatenating the generators. The question above can be then restated as follows: Does every mixing coded system have a set of genertaors $(w_n)_{n\in\mathbb{N}}$ such that $\text{gcd} \{|w_n| : n\in\mathbb{N}\}=1$? ($|w|$ is the length of a word (block) $w$). | |
| Feb 9, 2014 at 23:21 | history | edited | Dominik Kwietniak | CC BY-SA 3.0 |
I have formulated the question in a more precise way.
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| Feb 7, 2014 at 11:27 | history | asked | Dominik Kwietniak | CC BY-SA 3.0 |