Timeline for When do disjoint sequences with bounded consecutive differences exist?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| S Nov 11, 2023 at 9:04 | history | bounty ended | CommunityBot | ||
| S Nov 11, 2023 at 9:04 | history | notice removed | CommunityBot | ||
| Nov 10, 2023 at 10:24 | comment | added | Alex Ravsky | To ensure the needed multiplicities we have to start count these numbers from at least $\max\{a_1^1,\dots,a_n^1\}$. | |
| Nov 10, 2023 at 10:13 | answer | added | Alex Ravsky | timeline score: 1 | |
| Nov 3, 2023 at 19:19 | answer | added | Jean-Armand Moroni | timeline score: 1 | |
| Nov 3, 2023 at 12:01 | history | edited | user242318 | CC BY-SA 4.0 |
Provided necessary condition
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| Nov 3, 2023 at 12:00 | comment | added | user242318 | The necessity of $\sum_i 1/N_i \leq 1$ is easy to see from counting the numbers used in the sequences $a_i$ up to $N_1 \cdot \dots \cdot N_n$. | |
| Nov 3, 2023 at 11:09 | answer | added | Command Master | timeline score: 4 | |
| Nov 3, 2023 at 9:20 | comment | added | Alex Ravsky | @Jean-ArmandMoroni I expect I can easily prove that this condition is necessary. On the other hand, it is not sufficient. For instance, it is easy to show that for $(N_1,N_2,N_3)=(2,3,7)$ there are no required sequences. | |
| S Nov 3, 2023 at 7:13 | history | bounty started | user242318 | ||
| S Nov 3, 2023 at 7:13 | history | notice added | user242318 | Canonical answer required | |
| Oct 10, 2023 at 13:33 | comment | added | Jean-Armand Moroni | I would bet that the correct condition is: $\sum_i \frac 1 {N_i} \le 1$, but no proof in mind. | |
| Oct 10, 2023 at 13:18 | history | edited | user242318 | CC BY-SA 4.0 |
Unclear formulation
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| Oct 10, 2023 at 13:16 | comment | added | user242318 | @Jean-ArmandMoroni : I mean the for each sequence $a_i=(a_i^1, a_i^2, \dots)$ we have $a_i^{j+1} - a_i^j \leq N_i$. | |
| Oct 10, 2023 at 13:11 | comment | added | Jean-Armand Moroni | Could you please explain what you mean by "with consecutive differences bounded by $N_1, N_2, \dots, N_n$"? | |
| Oct 10, 2023 at 12:45 | history | asked | user242318 | CC BY-SA 4.0 |