Timeline for Sets of residues with only a single intersection under translation
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 13, 2020 at 17:26 | vote | accept | BPP | ||
| Aug 13, 2020 at 17:06 | comment | added | Max Alekseyev | @GerhardPaseman: We should have $j_i$ as divisors of $n$ as otherwise "negative" differences would not be multiples of $j_i$. Ideally $n$ should be LCM of the $j_i$. For $k=3$ and $n=200$, we have with necessity that $m\leq 34$. See my answer for details. | |
| Aug 13, 2020 at 14:33 | answer | added | Max Alekseyev | timeline score: 1 | |
| Aug 13, 2020 at 5:11 | comment | added | BPP | I think the sets work for $n\ge m$. I've edited my question to fix this. Thanks for pointing it out. | |
| Aug 13, 2020 at 5:10 | history | edited | BPP | CC BY-SA 4.0 |
fix wrong inequality
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| Aug 13, 2020 at 4:22 | comment | added | Gerhard Paseman | Have you tried k different coprime integers j_i?. Then for N less than the product of the j_i, the sets which are 0 mod j_i and have about N/j_i elements each should work. For N=200, the numbers 5,6, and 7 do a nice job. I'm not sure you will do much better than m=200/7 for k=3 and N=200. Gerhard "Residue Classes Can Be Shifty" Paseman, 2020.08.12. | |
| Aug 13, 2020 at 4:18 | comment | added | Max Alekseyev | It is necessary and sufficient that for any nonzero $d\in\Bbb Z/n\Bbb Z$, there exists $i\in\{1,2,\dots,k\}$ such that $d\notin (A_i-A_i)$. | |
| Aug 13, 2020 at 3:58 | history | edited | Max Alekseyev | CC BY-SA 4.0 |
m was mixed with k
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| Aug 12, 2020 at 23:04 | history | edited | BPP | CC BY-SA 4.0 |
added 5 characters in body
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| S Aug 12, 2020 at 21:11 | history | edited | BPP | CC BY-SA 4.0 |
Math Jaxed
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| S Aug 12, 2020 at 21:11 | history | suggested | Daniele Tampieri | CC BY-SA 4.0 |
Math Jaxed
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| Aug 12, 2020 at 21:05 | review | Suggested edits | |||
| S Aug 12, 2020 at 21:11 | |||||
| Aug 12, 2020 at 20:26 | review | First posts | |||
| Aug 12, 2020 at 21:43 | |||||
| Aug 12, 2020 at 20:24 | history | asked | BPP | CC BY-SA 4.0 |