Timeline for singly-generated monoids in mathematics
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Feb 18, 2011 at 22:59 | vote | accept | James Propp | ||
| Feb 6, 2011 at 4:25 | comment | added | Gerhard Paseman | @Andreas, yes. There are a wealth of examples of functions which are monotonic decreasing or constant with respect to some well-ordered ranking on the domain=range of the function. In some cases, it is useful to restrict the domain to those objects whose rank is at most some ordinal. This is why I backpedaled on the Collatz function by parenthetically mentioning restriction. Gerhard "Ask Me About System Design" Paseman, 2011.02.05 | |
| Feb 4, 2011 at 3:24 | comment | added | Tracy Hall | Does running LaTeX count as an important operation? | |
| Feb 3, 2011 at 11:05 | comment | added | Andreas Blass | @Gerhard Paseman: I understood the question as being about situations where two iterates of the whole function $s$ agree. In the Collatz case, this would mean not only that the iteration, started from any integer, eventually enters a loop, but that there's a uniform bound on how many steps that takes (which is clearly not the case). | |
| Feb 3, 2011 at 3:37 | answer | added | Tony Huynh | timeline score: 5 | |
| Feb 3, 2011 at 3:17 | comment | added | S. Carnahan♦ | Do you specifically want to exclude involutions (satisfying $sss = s$) and other finite order automorphisms from consideration? | |
| Feb 3, 2011 at 0:37 | answer | added | Steve Lack | timeline score: 18 | |
| Feb 2, 2011 at 23:55 | comment | added | Martin Brandenburg | @James: Very interesting question! 1+ | |
| Feb 2, 2011 at 20:10 | comment | added | Joe Silverman | Not sure if this is what you have in mind, but in dynamics one looks at preperiodic points, which are points satisfying the relation $s^n(t) = s^m(t)$, where $s$ is (say) a rational function, exponentiation is iteration, and $n>m$. So the relation $sss=ss$ isn't satisfied identically, but it defines an interesting locus. PS That's a very amusing story. | |
| Feb 2, 2011 at 20:07 | comment | added | Gerhard Paseman | Collatz's function (on certain subsets of the integers), almost surely. (Wish I had a proof.) There are similar examples, although across the entire domain of the function no single such relation holds. Gerhard "Ask Me About System Design" Paseman, 2011.02.02 | |
| Feb 2, 2011 at 19:58 | history | asked | James Propp | CC BY-SA 2.5 |