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Reducing the problem from k+1 runners to k runner by assuming that one of the runner has speed zero imposes on the first spot that some runners may have negative speeds. It is stated that one can restrict to the case of k "positive integers" as proven in the paper of Bohman, Holzman, Kleitman. I cannot see the argument why it is possible to restrict to positive (integer) speeds nor can I find this argument for positivity in Bohman, Holzman, Kleitman. To clarify, the argument why one can restrict to rational (hence integer) speeds is contained in the mentioned paper. — Preceding unsigned comment added by 134.147.253.243 ( talk) 15:32, 20 November 2018 (UTC)
The table with known results, and the year when they were proved, contradict the dates cited on the page at the Open Problem Garden. In any case, the table needs inline citations. Hermel ( talk) 10:17, 20 March 2009 (UTC)
The results for k <= 3 should be added, at least in the "Known results" box. For k = 0 and 1 the result is trivial (t=0 and t=v2-v1), and I can add it myself, but k = 2 could have its own explanatory section. MestreLion ( talk) 15:41, 28 February 2013 (UTC)
Not substituting k+1 for k is just stupid. I'm changing that shit.
Why is it that any proof for k larger than 3, automatically proves it for k=3? - DPizzo ( talk) 23:22, 21 August 2013 (UTC) Just add runner speed infinitesimally small. It is trivial. — Preceding unsigned comment added by Mtheorylord ( talk • contribs) 02:06, 11 August 2016 (UTC)
what are the speeds for each of the runners in the gif animation to the right? — Preceding unsigned comment added by 69.171.166.1 ( talk) 22:32, 8 September 2013 (UTC)
With respect to this: it is a true statement. Its truth is the underlying reason that this article begins "in number theory". But (1) it is uncited, and (2) it is certainly not part of the formulation of the problem (which is the topic of the section to which it was added). With a citation, we could certainly try to fit it in somewhere else. -- JBL ( talk) 00:41, 1 November 2021 (UTC)
GA toolbox |
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Reviewing |
Reviewer: David Eppstein ( talk · contribs) 01:23, 22 May 2022 (UTC)
I have edited the article, but they were very minor edits, long ago, so I am not a significant contributor.
GA review – see WP:WIAGA for criteria
I'll put this on hold to allow you time to perform these edits. Please ping me here when you are ready for another reading. —
David Eppstein (
talk)
07:28, 22 May 2022 (UTC)
@ Ovinus: Looking better; here are a few more comments.
"she can be made stationary by subtracting her speed": Why not use the gender-free singular they again, as was already used at the start of the same section?
"how well multiple real numbers can be simultaneously approximated": what is the actual implication for simultaneous approximation of this conjecture? Is it easy to explain?
Let
Is or ?
is his (idiosyncratic?) way of the nonnegative distance to the nearest integer. That's pretty much the exact statement of our problem, restricted to integers, just in symbols. Then (I is for irrationals): This problem of the one-dimensional Diophantine approximation is equivalent to the following problem of the simultaneous Diophantine approximation:
Is or ?
In words I guess this means: "We conjecture that, when simultaneously approximating a set of irrational numbers by fractions of some denominator (increasing from 1), at some point you will have an error of at least across all approximations." Should I include this? For now I've removed the vague description of the conjecture. (I thought it was some cool generalization of Dirichlet's approximation theorem or something, but doesn't seem to be.)
"A centered copy of C is placed": The switch from imperative in the previous sentence to passive here feels awkward. Why not stick with imperative?
"every point with positive half-integer coordinates. A ray from the origin into the positive orthant (in other words, directed positively in every dimension)": what is the point of requiring positivity here? Is it only to avoid axis-perpendicular rays?
"there are gaps": this term has not been explained. Maybe replace this by something like "some rays avoid all copies of C?" Or explain what a gap is.
"The lonely runner conjecture implies that the minimum k for which G admits a proper k-regular coloring (i.e., each node is colored differently than its adjacencies) for some step value is at most | D | + 1.": You're overcomplicating, by saying "the extremum of values with this property is x" where you could say "x has this property", again. The lonely runner conjecture implies that G admits a proper (|D|+1)-coloring.
"Suppose f is further restricted to positive integers. The lonely runner conjecture implies that, if f attains at most k different values, then G has a nowhere-zero flow with values only in { 1 , 2 , … , k }." => "The lonely runner conjecture implies that, when a graph has a nowhere-zero flow with k distinct integer values, it has a nowhere-zero flow with values in {1,2, ..., k}." No need to apply restrictions to classes of functions only to restrict them again later. No need to name the flow that we are going to replace.
"at which he is strictly more": again, why not they?
— David Eppstein ( talk) 06:29, 25 May 2022 (UTC)
The result was: promoted by
SL93 (
talk)
22:25, 1 June 2022 (UTC)
Improved to Good Article status by Ovinus ( talk). Self-nominated at 18:35, 26 May 2022 (UTC).
General: Article is new enough and long enough |
---|
Policy: Article is sourced, neutral, and free of copyright problems |
---|
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Hook: Hook has been verified by provided inline citation |
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QPQ: None required. |
Overall:
My only concern is that the article is technical and difficult to understand. The lede to the article does give an intelligible summary, though. I am a new reviewer. Second opinion welcome. —
rsjaffe
🗣️
21:15, 27 May 2022 (UTC)
![]() | Lonely runner conjecture has been listed as one of the
Mathematics good articles under the
good article criteria. If you can improve it further,
please do so. If it no longer meets these criteria, you can
reassess it. Review: May 26, 2022. ( Reviewed version). |
![]() | A fact from Lonely runner conjecture appeared on Wikipedia's
Main Page in the
Did you know column on 7 June 2022 (
check views). The text of the entry was as follows:
| ![]() |
![]() | This article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Reducing the problem from k+1 runners to k runner by assuming that one of the runner has speed zero imposes on the first spot that some runners may have negative speeds. It is stated that one can restrict to the case of k "positive integers" as proven in the paper of Bohman, Holzman, Kleitman. I cannot see the argument why it is possible to restrict to positive (integer) speeds nor can I find this argument for positivity in Bohman, Holzman, Kleitman. To clarify, the argument why one can restrict to rational (hence integer) speeds is contained in the mentioned paper. — Preceding unsigned comment added by 134.147.253.243 ( talk) 15:32, 20 November 2018 (UTC)
The table with known results, and the year when they were proved, contradict the dates cited on the page at the Open Problem Garden. In any case, the table needs inline citations. Hermel ( talk) 10:17, 20 March 2009 (UTC)
The results for k <= 3 should be added, at least in the "Known results" box. For k = 0 and 1 the result is trivial (t=0 and t=v2-v1), and I can add it myself, but k = 2 could have its own explanatory section. MestreLion ( talk) 15:41, 28 February 2013 (UTC)
Not substituting k+1 for k is just stupid. I'm changing that shit.
Why is it that any proof for k larger than 3, automatically proves it for k=3? - DPizzo ( talk) 23:22, 21 August 2013 (UTC) Just add runner speed infinitesimally small. It is trivial. — Preceding unsigned comment added by Mtheorylord ( talk • contribs) 02:06, 11 August 2016 (UTC)
what are the speeds for each of the runners in the gif animation to the right? — Preceding unsigned comment added by 69.171.166.1 ( talk) 22:32, 8 September 2013 (UTC)
With respect to this: it is a true statement. Its truth is the underlying reason that this article begins "in number theory". But (1) it is uncited, and (2) it is certainly not part of the formulation of the problem (which is the topic of the section to which it was added). With a citation, we could certainly try to fit it in somewhere else. -- JBL ( talk) 00:41, 1 November 2021 (UTC)
GA toolbox |
---|
Reviewing |
Reviewer: David Eppstein ( talk · contribs) 01:23, 22 May 2022 (UTC)
I have edited the article, but they were very minor edits, long ago, so I am not a significant contributor.
GA review – see WP:WIAGA for criteria
I'll put this on hold to allow you time to perform these edits. Please ping me here when you are ready for another reading. —
David Eppstein (
talk)
07:28, 22 May 2022 (UTC)
@ Ovinus: Looking better; here are a few more comments.
"she can be made stationary by subtracting her speed": Why not use the gender-free singular they again, as was already used at the start of the same section?
"how well multiple real numbers can be simultaneously approximated": what is the actual implication for simultaneous approximation of this conjecture? Is it easy to explain?
Let
Is or ?
is his (idiosyncratic?) way of the nonnegative distance to the nearest integer. That's pretty much the exact statement of our problem, restricted to integers, just in symbols. Then (I is for irrationals): This problem of the one-dimensional Diophantine approximation is equivalent to the following problem of the simultaneous Diophantine approximation:
Is or ?
In words I guess this means: "We conjecture that, when simultaneously approximating a set of irrational numbers by fractions of some denominator (increasing from 1), at some point you will have an error of at least across all approximations." Should I include this? For now I've removed the vague description of the conjecture. (I thought it was some cool generalization of Dirichlet's approximation theorem or something, but doesn't seem to be.)
"A centered copy of C is placed": The switch from imperative in the previous sentence to passive here feels awkward. Why not stick with imperative?
"every point with positive half-integer coordinates. A ray from the origin into the positive orthant (in other words, directed positively in every dimension)": what is the point of requiring positivity here? Is it only to avoid axis-perpendicular rays?
"there are gaps": this term has not been explained. Maybe replace this by something like "some rays avoid all copies of C?" Or explain what a gap is.
"The lonely runner conjecture implies that the minimum k for which G admits a proper k-regular coloring (i.e., each node is colored differently than its adjacencies) for some step value is at most | D | + 1.": You're overcomplicating, by saying "the extremum of values with this property is x" where you could say "x has this property", again. The lonely runner conjecture implies that G admits a proper (|D|+1)-coloring.
"Suppose f is further restricted to positive integers. The lonely runner conjecture implies that, if f attains at most k different values, then G has a nowhere-zero flow with values only in { 1 , 2 , … , k }." => "The lonely runner conjecture implies that, when a graph has a nowhere-zero flow with k distinct integer values, it has a nowhere-zero flow with values in {1,2, ..., k}." No need to apply restrictions to classes of functions only to restrict them again later. No need to name the flow that we are going to replace.
"at which he is strictly more": again, why not they?
— David Eppstein ( talk) 06:29, 25 May 2022 (UTC)
The result was: promoted by
SL93 (
talk)
22:25, 1 June 2022 (UTC)
Improved to Good Article status by Ovinus ( talk). Self-nominated at 18:35, 26 May 2022 (UTC).
General: Article is new enough and long enough |
---|
Policy: Article is sourced, neutral, and free of copyright problems |
---|
|
Hook: Hook has been verified by provided inline citation |
---|
|
QPQ: None required. |
Overall:
My only concern is that the article is technical and difficult to understand. The lede to the article does give an intelligible summary, though. I am a new reviewer. Second opinion welcome. —
rsjaffe
🗣️
21:15, 27 May 2022 (UTC)