Timeline for EGZ theorem (Erdős-Ginzburg-Ziv)
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 7, 2021 at 11:07 | comment | added | richrow | The other way, probably, is taking derivatives. For any sequence $i_1,\ldots,i_{p-1}\in\{1,2,\ldots,2p-1\}$ consider $\left(\prod_{k=1}^{p-1}\frac{\partial}{\partial a_{i_k}}\right)F$. If i'm not mistaken this equals $(p-1)!\cdot\binom{2p-1-m}{p-m}$ ($(p-1)!$ times the number of $p$-element subsets containing $\{i_1,\ldots,i_{p-1}\}$). However, I think that both approaches are basically the same. | |
| Jan 7, 2021 at 11:07 | comment | added | richrow | Well, Ithink that this verification isn't really difficult (the coefficient of $\prod_{i=1}^{m}a_i^{k_i}$, where $\sum_{i=1}^{m}k_i=p-1$ is $\frac{(p-1)!}{k_1!\ldots k_m!}\cdot\binom{2p-1-m}{p-m}$ which is zero modulo $p$). | |
| Jul 25, 2020 at 13:18 | comment | added | richrow | For $n=p$, where $p$ is prime, we can consider the following sum $F(a_1,\ldots,a_{2p-1})=\sum_{A}s(A)^{p-1}$, where $A$ runs over all $p$-element subsets of $\{a_1,a_2,\ldots,a_{2p-1}\}$. It can be verified that all coefficents of $F$ as polynomial of $a_i$'s are zero modulo $p$. On the other hand, if the claim of the theorem is false, then $F(a_1,\ldots,a_{2p-1})\equiv\binom{2p-1}{p-1}\not\equiv 0\pmod p$. This is not an application of Chevalley-Warning, but in the same spirit, I think. (Here $s(A)$ is the sum of elenebts of $A$) | |
| Oct 24, 2018 at 5:07 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Erdos -> Erdős + clean-up
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| Oct 24, 2018 at 1:13 | history | edited | darij grinberg | CC BY-SA 4.0 |
added 9 characters in body
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| Mar 1, 2010 at 3:54 | vote | accept | Portland | ||
| Mar 1, 2010 at 3:54 | vote | accept | Portland | ||
| Mar 1, 2010 at 3:54 | |||||
| Mar 1, 2010 at 3:54 | vote | accept | Portland | ||
| Mar 1, 2010 at 3:54 | |||||
| Mar 1, 2010 at 1:45 | answer | added | Hailong Dao | timeline score: 10 | |
| Feb 28, 2010 at 23:12 | answer | added | Gjergji Zaimi | timeline score: 13 | |
| Feb 28, 2010 at 23:07 | comment | added | Pete L. Clark | Good question, but I have to comment that I find the proof using Chevalley-Warning (the only one I know) to be extremely beautiful. | |
| Feb 28, 2010 at 22:58 | history | asked | Portland | CC BY-SA 2.5 |