Timeline for Shortest almost trivial element of free group
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14 at 23:51 | comment | added | YCor | Precisely, by induction, given $n\ge 2$, write $m=\lceil n/2\rceil$, and let $c_m$, $c_{n-m}$ be minimizing words on $m$ and $n-m\in\{m,m-1\}$ variables. Then $c_n(x_1,\dots,x_n)=[c_m(x_1,\dots,x_m),c_{n-m}(x_{m+1},\dots,x_n)]$ is minimizing, with $c_1(x_1)=x_1$. So $c_2(x,y)=[x,y]$, $c_3(x,y,z)=[[x,y],z]$, $c_4(\dots)=[[x,y],[z,w]]$, $c_5(\dots)=[[[x,y],z],[w,t]]$, etc., yields a minimizing sequence. | |
| Feb 14 at 21:58 | history | edited | Sean Eberhard | CC BY-SA 4.0 |
Removed "not nested". They are nested!
|
| Feb 14 at 19:30 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
added 97 characters in body
|
| Feb 14 at 19:26 | vote | accept | Anton Petrunin | ||
| Feb 14 at 14:20 | comment | added | Sean Eberhard | @YCor Yes it is. | |
| Feb 14 at 14:03 | history | edited | LSpice | CC BY-SA 4.0 |
Link to survey
|
| Feb 14 at 12:32 | comment | added | YCor | So, is this oeis.org/A073121 ? | |
| Feb 14 at 12:16 | history | answered | Sean Eberhard | CC BY-SA 4.0 |