Timeline for Examples of combinatorial problems where the only known solutions, or most "natural" solutions, use representation theory?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 4 at 18:07 | comment | added | Sam Hopkins | @DavidESpeyer: Nice! So it is possible to give a proof avoiding character theory. | |
| Nov 4 at 18:05 | comment | added | David E Speyer | This is a special case (namely, the case $x = e$) of a question math.stackexchange.com/questions/365476/… I asked at math.SE and which got good answers: | |
| Nov 4 at 12:54 | comment | added | Timothy Chow | I'm not sure it's worth posting as a separate answer, because it's not a problem that anyone would think to study without already knowing the representation theory of the symmetric group. But the statement is this: if we multiply the Schur function $s_\lambda$ by the product of the hook lengths of $\lambda$, and express the result in terms of power-sum symmetric functions, then the coefficients are integers. | |
| Nov 4 at 10:13 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Nov 4 at 0:01 | comment | added | Timothy Chow | I didn't notice that the numbering of the supplementary problems in the second edition of EC2 differs from the numbering in the online PDF that you linked to. When I said "problem 43" I meant problem 43 in the second edition of EC2. In the online PDF, this is problem 42. | |
| Nov 3 at 23:52 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
added 135 characters in body
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| Nov 3 at 23:25 | comment | added | Timothy Chow | See also supplementary problem 43 and Theorem A2.2.2. | |
| Nov 3 at 22:49 | history | rollback | LSpice |
Rollback to Revision 1
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| Nov 3 at 22:48 | history | edited | LSpice | CC BY-SA 4.0 |
Name of "here" and "here"
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| Nov 3 at 16:50 | history | answered | Sam Hopkins | CC BY-SA 4.0 |