Timeline for In arbitrary cyclic polygon then $\sum_{i<j} x_{ij}^\alpha \ge \sum_{i<j} y_{ij}^\alpha $
Current License: CC BY-SA 4.0
35 events
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| Aug 24 at 9:08 | answer | added | Fedor Petrov | timeline score: 1 | |
| Aug 22 at 17:35 | answer | added | Toni Mhax | timeline score: 1 | |
| Aug 21 at 23:09 | comment | added | Đào Thanh Oai | I am very happy. Please publish in on answer box or a journal. @ToniMhax | |
| Aug 21 at 16:49 | comment | added | Toni Mhax | Hy, i have a proof for a triangle, it doesn't seem generalisable, but I guess this proves the inequality for any real $\alpha\le 2$. Let me know if this is of interest. Ty | |
| Aug 21 at 15:03 | comment | added | Đào Thanh Oai | @FedorPetrov I mean $B_1, B_2,…,B_n$ be $n$ points lie on circle $(O)$ | |
| Aug 21 at 12:41 | comment | added | Fedor Petrov | This holds for $\alpha=2$ since $\sum y_{ij}^2=n-|\sum b_i|^2$, where $b_i$ is a radius-vector of $B_i$. Thus, we would prove the result for given $n$ if we manage to find non-negative coefficients $c_1\ldots,c_{n-1}$ and real $c_0$ such that $|1-z|^\alpha \leqslant c_0+\sum_{k=1}^{n-1} c_k|1-z^k|^2$ for every $z$ on the unit circle, with equality holding for $z=e^{2 \pi i m/n}$, $m=1,2,\ldots n-1$. | |
| Aug 21 at 12:34 | comment | added | Fedor Petrov | @fedja Ok, I just would not call it a polygon. Never mind. | |
| Aug 21 at 11:41 | comment | added | fedja | @FedorPetrov List vertices in a wrong order. It will change nothing in the problem statement, of course :-) | |
| Aug 21 at 11:31 | comment | added | Fedor Petrov | How an ibscribed polygon may be not convex? | |
| Aug 21 at 3:24 | history | edited | Đào Thanh Oai |
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| S May 2, 2021 at 13:01 | history | bounty ended | CommunityBot | ||
| S May 2, 2021 at 13:01 | history | notice removed | CommunityBot | ||
| S Apr 24, 2021 at 11:39 | history | bounty started | Đào Thanh Oai | ||
| S Apr 24, 2021 at 11:39 | history | notice added | Đào Thanh Oai | Authoritative reference needed | |
| S Jul 4, 2020 at 18:07 | history | bounty ended | CommunityBot | ||
| S Jul 4, 2020 at 18:07 | history | notice removed | CommunityBot | ||
| S Jun 26, 2020 at 16:31 | history | bounty started | Đào Thanh Oai | ||
| S Jun 26, 2020 at 16:31 | history | notice added | Đào Thanh Oai | Authoritative reference needed | |
| S Aug 16, 2018 at 17:01 | history | bounty ended | CommunityBot | ||
| S Aug 16, 2018 at 17:01 | history | notice removed | CommunityBot | ||
| S Aug 8, 2018 at 15:17 | history | bounty started | Đào Thanh Oai | ||
| S Aug 8, 2018 at 15:17 | history | notice added | Đào Thanh Oai | Authoritative reference needed | |
| S Aug 4, 2018 at 3:01 | history | bounty ended | CommunityBot | ||
| S Aug 4, 2018 at 3:01 | history | notice removed | CommunityBot | ||
| Jul 28, 2018 at 0:55 | history | edited | Đào Thanh Oai | CC BY-SA 4.0 |
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| Jul 27, 2018 at 1:56 | history | edited | Đào Thanh Oai | CC BY-SA 4.0 |
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| S Jul 27, 2018 at 1:54 | history | bounty started | Đào Thanh Oai | ||
| S Jul 27, 2018 at 1:54 | history | notice added | Đào Thanh Oai | Authoritative reference needed | |
| Jul 12, 2018 at 14:47 | comment | added | Tran Quang Hung | That's right Mr Dao, thank you very much. I thought the regular polygon was convex but this is not really. | |
| Jul 12, 2018 at 14:12 | comment | added | Đào Thanh Oai | @TranQuangHung I don't think that | |
| Jul 12, 2018 at 9:27 | comment | added | Tran Quang Hung | Dear Mr Dao, I think polygon $B_1B_2...B_n$ need be convex? | |
| Jul 12, 2018 at 8:15 | history | edited | Đào Thanh Oai | CC BY-SA 4.0 |
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| Jul 12, 2018 at 8:06 | history | edited | Đào Thanh Oai | CC BY-SA 4.0 |
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| Jul 12, 2018 at 5:55 | history | edited | Đào Thanh Oai | CC BY-SA 4.0 |
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| Jul 12, 2018 at 5:39 | history | asked | Đào Thanh Oai | CC BY-SA 4.0 |