Timeline for list of Hall basis
Current License: CC BY-SA 3.0
15 events
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| May 24, 2012 at 14:38 | comment | added | Adrien | I agree that tables are usefull, the point is that SAGE can generate it :) And you don't have to instal it, either : you can go to sagenb.org and copy/paste the above code. By the way answering you made me find this bug and I just submitted a fix, so it was useful ! | |
| May 24, 2012 at 13:56 | comment | added | Jim Stasheff | I had no idea that Omar's suggestion would do the computation and display the results rather than being software I could download and compute. A marvelous resource! I googled a bit more until I found CoRoPa, which does compute it.) – Omar Antolín-Camarena 22 hours ago I'd tried gogling but got nowhere near! | |
| May 24, 2012 at 13:25 | comment | added | Jim Stasheff | Many thanks for information and enlightenment. Will have a look to see if I can find a list up through 5-fold brackets. Even with SAGE, tables are still useful. | |
| May 23, 2012 at 15:25 | comment | added | Adrien | It seems to me that Hall basis differ only in the (rather arbitrary) choice of some total ordering on the set of previously computed elements. I think Hall gave some specific choice in his paper, which is maybe what is called "the" Hall basis, while the Lyndon one is "a" Hall basis basically relying on the lexicographic order. Hence, I would say that the Hall basis is the first one historically speaking, but doesn't enjoy other specific properties which would make it more usefull than another one. of course I may be wrong. | |
| May 23, 2012 at 15:08 | comment | added | Omar Antolín-Camarena | (I should say, my first thought to check if SAGE had a function to compute the Hall basis and I was a little surprised to see in the docs that it had the StandardBracketedLyndonWords function, but no function for the Hall basis. Since I thought Stasheff meant the other basis specifically --which may or may not be true-- I googled a bit more until I found CoRoPa, which does compute it.) | |
| May 23, 2012 at 15:05 | comment | added | Omar Antolín-Camarena | With the name I learned (which I'm not sure are standard), there is something called a "generalized Hall basis" of which both the Lyndon and Hall basis are examples. But in the terminology I learned, the Hall basis is definitely a specific basis and is different from the Lyndon basis. Just to repeat, the web app I linked computes the thing I was told to call the Hall basis. | |
| May 23, 2012 at 14:36 | history | edited | Adrien | CC BY-SA 3.0 |
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| May 23, 2012 at 13:24 | history | edited | Adrien | CC BY-SA 3.0 |
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| May 23, 2012 at 12:49 | history | edited | Adrien | CC BY-SA 3.0 |
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| May 23, 2012 at 12:35 | history | edited | Adrien | CC BY-SA 3.0 |
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| May 23, 2012 at 11:54 | history | edited | Adrien | CC BY-SA 3.0 |
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| May 23, 2012 at 11:49 | history | edited | Adrien | CC BY-SA 3.0 |
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| May 23, 2012 at 11:21 | comment | added | Adrien | In fact I'm not sure there is "one" Hall basis, but rather many basis associated to so-called "Hall Sets" (en.wikipedia.org/wiki/Hall_set#Hall_sets) of which the set of Lyndon word is a particular (algorithmically efficient) example. | |
| May 23, 2012 at 10:09 | comment | added | Omar Antolín-Camarena | This gives you the Lyndon basis, not the Hall basis. Compare with the output of this webapp: coropa.sourceforge.net/#cgi | |
| May 23, 2012 at 8:05 | history | answered | Adrien | CC BY-SA 3.0 |