Timeline for What is the combinatorial rule from the array of integers to the semistandard Young tableau?
Current License: CC BY-SA 4.0
12 events
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| Dec 23, 2020 at 18:44 | comment | added | Sam Hopkins | @JianrongLi: Thanks, the question is much better now (and interesting)! | |
| Dec 23, 2020 at 18:44 | history | edited | Jianrong Li | CC BY-SA 4.0 |
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| Dec 23, 2020 at 18:41 | comment | added | Jianrong Li | @Sam Hopkins, I added the method to produce $P_i$. Thanks a lot. | |
| Dec 23, 2020 at 18:37 | history | edited | Jianrong Li | CC BY-SA 4.0 |
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| Dec 23, 2020 at 15:10 | comment | added | Sam Hopkins | But what was the method by which you produced the $P_i$? | |
| Dec 23, 2020 at 7:55 | comment | added | Jianrong Li | @Sam Hopkins, thank you very much. | |
| Dec 23, 2020 at 7:54 | comment | added | Jianrong Li | @Per Alexandersson, thanks. Yes, exactly. The rule I know to get T_i from P_i is not complete. So I am trying to find a some more straightforward rule. | |
| Dec 23, 2020 at 5:15 | comment | added | Sam Hopkins | I think that Jianrong's point when they say the arrays "correspond" to the SSYT is that the contents (i.e., numbers of each entry) match up the arrays and tableaux. Of course, promotion rotates content, just like adding $1$ mod $9$ to each entry does. | |
| Dec 22, 2020 at 21:19 | comment | added | Per Alexandersson | I do not think I understand your question then - it sounds that you have some uniform rule to get T_i from the T_i, and is looking for some more straightforward one... One way to produce SSYTs from a list of numbers is to use RSK insertion. Another way, to get pairs of SSYTs from integer arrays is also to use a variant of RSK insertion... | |
| Dec 22, 2020 at 21:04 | comment | added | Jianrong Li | @Per Alexandersson, thank you very much. For $P_1$, we can first reorder each row from small to large. Then we reorder each column from small to large. And we move some numbers down when a column is not strictly increasing. But this does not work for $P_3$. We need to interchange $7$ and $8$ in the end. Do you have some uniform rule which work for every $P_i$? | |
| Dec 22, 2020 at 18:48 | comment | added | Per Alexandersson | In what way can you get the SSYT from the arrays? There are several ways to produce SSYTs from arrays... | |
| Dec 22, 2020 at 17:05 | history | asked | Jianrong Li | CC BY-SA 4.0 |