Timeline for Subwords of cube-free binary words
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 21, 2012 at 22:01 | comment | added | Gerhard Paseman | I observed that by the time I got to 12 characters, most words had 5 of the 6 allowable triplets. It might be interesting to see the stats on length vs number of k-length subwords covered. Gerhard "Ask Me About System Design" Paseman, 2012.09.21 | |
| Sep 21, 2012 at 21:24 | history | edited | Douglas Zare | CC BY-SA 3.0 |
Added pairs of avoided words of length 4.
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| Sep 21, 2012 at 0:31 | vote | accept | JRN | ||
| Sep 21, 2012 at 0:02 | comment | added | JRN | The number of cube-free binary words of length $n$, for $1\le n\le 80$ can be found in table 1 (page 600) of mdpi.com/1099-4300/10/4/590. Your figure of 230800 words of length 30 agrees with theirs. | |
| Sep 20, 2012 at 15:45 | comment | added | Gerhard Paseman | The number of cubefree words of length 30 is less than twice the 29th Fibonacci number, which is less than 10*7^6, so it is believable. Gerhard "Ask Me About Crude Estimates" Paseman, 2012.09.20 | |
| Sep 20, 2012 at 15:26 | comment | added | Douglas Zare | My counts of cube-free words agree with oeis.org/A028445 which oddly only has the counts up to length $28$. | |
| Sep 20, 2012 at 15:19 | history | answered | Douglas Zare | CC BY-SA 3.0 |