# Talk:Telephone number (mathematics)

Reading this article got me thinking and I just have one question: According to the article the nth telephone number is the number of self-inverse permutations on n elements. If I'm not mistaken, a self-inverse permutation on n elements is essentially an n by n matrix such that every line and every column contains exactly one 1 entry and only 0's otherwise. Accordingly, there should be according to this sequence only 4 such 3 by 3 matrices. However, I was able to find 6:

  
    
      
        
          
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    {\displaystyle {\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}},{\begin{bmatrix}1&0&0\\0&0&1\\0&1&0\end{bmatrix}},{\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}},{\begin{bmatrix}0&1&0\\0&0&1\\1&0&0\end{bmatrix}},{\begin{bmatrix}0&0&1\\0&1&0\\1&0&0\end{bmatrix}},{\begin{bmatrix}0&0&1\\1&0&0\\0&1&0\end{bmatrix}}}
  

Could you tell me what my mistake was?--Carabinieri (talk) 21:31, 30 March 2012 (UTC)

The condition that each row and column has exactly one nonzero defines an arbitrary permutation, not necessarily a self-inverse one. The self-inverse permutations correspond to the symmetric matrices. Your fourth and sixth matrices are not symmetric and do not correspond to involutions. (Or, yet another way of saying the same thing, they do not square to the identity matrix.) —David Eppstein (talk) 22:03, 30 March 2012 (UTC)
Thanks. I thought I'd read somewhere that all permutation matrices were self-inverse, but I guess that doesn't really make a whole lot of sense.--Carabinieri (talk) 22:13, 30 March 2012 (UTC)
They're all idempotent, though — maybe that's what you were remembering? —David Eppstein (talk) 22:39, 30 March 2012 (UTC)
Are you sure? According to that article, the only invertible idempotent matrix is the identity matrix. Yet, all permutation matrices are invertible.--Carabinieri (talk) 22:55, 30 March 2012 (UTC)
Sorry, wrong word. I meant that all of them can be taken to some power to reach the identity matrix. That power is not usually two though. —David Eppstein (talk) 18:04, 26 April 2012 (UTC)

The only "telephone number" that is also an actual US telephone number is 4809701440, and it apparently belongs to Studio Bravo Gary Babb. 68.44.132.25 (talk) 05:23, 22 February 2013 (UTC)

140.213.191.65 (talk) 21:50, 24 June 2021 (UTC)

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. ScottishFinnishRadish (talk) 21:55, 24 June 2021 (UTC)

This review is transcluded from Talk:Telephone number (mathematics)/GA1. The edit link for this section can be used to add comments to the review.
Reviewer: Praseodymium-141 (talk · contribs) 08:51, 6 August 2022 (UTC)

GA review (see here for what the criteria are, and here for what they are not)
It is reasonably well written: 
a (prose, spelling, and grammar): 
b (MoS for lead, layout, word choice, fiction, and lists): 

It is factually accurate and verifiable: 
a (reference section): 
b (citations to reliable sources): 
c (OR): 
d (copyvio and plagiarism): 

It is broad in its coverage: 
a (major aspects): 
b (focused): 

It follows the neutral point of view policy: 
Fair representation without bias: 

It is stable: 
No edit wars, etc.: 

It is illustrated by images and other media, where possible and appropriate: 
a (images are tagged and non-free content have non-free use rationales): 
b (appropriate use with suitable captions): 

Overall:
Pass/Fail: 

Hello, I'll be reviewing this article. 141Pr 08:51, 6 August 2022 (UTC)

@Praseodymium-141: Any progress? —David Eppstein (talk) 19:17, 21 August 2022 (UTC)
Yes. I'm currently very busy in real life and I'll try to finish the GA review as early as possible. I'm not sure how long though. 141Pr 09:15, 30 August 2022 (UTC)
Hello, I'll try to get back to the review today or tomorrow. Sorry for the delay. 141Pr 10:00, 29 September 2022 (UTC)
Sorry, but I'm not very knoweledgeable in this topic, so I might need to ask you some things about this topic that I'm not quite sure about. 141Pr 20:02, 11 October 2022 (UTC)


### Comments
1a:
No typographical errors seen, pass.
1b:
No comments yet.
2a:
No comments yet.
2b:
These sources are fine, but I'm not sure that this is the only information available. Can you please tell me if this is all the information available. I'll put this and 3a as a pass if it is fine.
2c:
No comments yet.
2d:
No comments yet.
3a:
No comments yet.
3b:
No comments yet.
4:
I haven't found any bias, probably pass.
5:
According to this article's history, there have been no edit wars since 2018. I'll put this as a pass.
6a:
No copyright issues seen, pass.
6b:
This is not a big problem, but I would suggest to move the pictures up a bit, so that it won't go into the next section. This is optional though, so you don't have to do it. 141Pr 10:03, 29 September 2022 (UTC)
Others:

Is there a navbox that this could be link to? (I'm not sure, so I'm asking) 141Pr 20:02, 11 October 2022 (UTC)
I strongly dislike navboxes. Especially Template:Classes of natural numbers, which lists an indiscriminate collection of far too many things, has been a magnet for problem editors pushing even more stuff into it, and doesn't currently link this article (nor should it be expanded). I don't think it provides any useful information to readers. It is just an excuse to link stuff for the purpose of linking stuff. —David Eppstein (talk) 21:16, 11 October 2022 (UTC)
Ok, that's fine, I was just asking because I wasn't sure about it. 141Pr 06:26, 12 October 2022 (UTC)
@Praseodymium-141: Except for a couple of brief questions that don't really address the GA criteria, there has been no review since you agreed to take this on 2 1/2 months ago. When can I expect a review? —David Eppstein (talk) 16:12, 21 October 2022 (UTC)

I don't think I'll be able to complete this review. Is there a way where I can reset the template so that another reviewer can do it? 141Pr 08:22, 22 October 2022 (UTC)
If no one else steps up for a few weeks, I can do it. That said, I'd like to see more reviewers at WP:GAN#MATH, so I won't take it just yet. Ovinus (talk) 16:54, 26 October 2022 (UTC)


### Ovinus
Alright. Less busy this week, and it's a short enough article, so should be done by tomorrow. Ovinus (talk) 04:57, 3 December 2022 (UTC)

GA review (see here for what the criteria are, and here for what they are not)
It is reasonably well written.
a (prose, spelling, and grammar):  b (MoS for lead, layout, word choice, fiction, and lists): 

It is factually accurate and verifiable.
a (reference section):  b (citations to reliable sources):  c (OR):  d (copyvio and plagiarism): 

It is broad in its coverage.
a (major aspects):  b (focused): 

It follows the neutral point of view policy.
Fair representation without bias: 

It is stable.
No edit wars, etc.: 

It is illustrated by images and other media, where possible and appropriate.
a (images are tagged and non-free content have non-free use rationales):  b (appropriate use with suitable captions): 

Overall:
Pass/Fail: 


#### Comments
Could we use "telephone pole" instead of "telephone line"? It's very easy to think of "telephone lines" as the wires/edges connecting the poles/vertices. Ovinus (talk) 04:57, 3 December 2022 (UTC)
What? That means something completely different and unrelated. A telephone line is, as telephone line tells us, "a single-user circuit on a telephone communication system". It's like an account on a social media system, the social media system of the early 20th century. It's a stand-in for the person using the line (or really for the family using the line, because this comes from the days when a phone and its number were something a whole family had rather than one per person). A telephone pole is a physical pole that holds up wires used to transmit telephone signals. It's a piece of hardware. —David Eppstein (talk) 07:07, 3 December 2022 (UTC)
Today I learned. Ovinus (talk) 19:11, 3 December 2022 (UTC)
Maybe we need to think about writing this in terminology that will be comprehensible to younger generations. A "phone line" used to mean the number you would dial (not press, dial), the wire into your house carrying the service for that number (a single twisted pair of wires extending all the way from your house to the telephone switching center), and the people you could reach by calling that number. Nowadays numbers are not associated with physical wires and houses. Unfortunately because of the title for this article it would not make sense to use the other meaning of "telephone number" for this concept, even though that might translate better to modern cell systems. —David Eppstein (talk) 19:34, 3 December 2022 (UTC)
Heh. None of the four friends I asked got it right, but maybe we're just unusually ignorant. I mean, one could simply phrase it as "how many ways can n people call each other?" but it loses the exclusivity implication and so would need more clarification. Another option is to give a short definition, with the pleasant side effect of our youth's edification. Ovinus (talk) 19:57, 3 December 2022 (UTC)
Okay, what you did is understandable and precise enough; nice. Ovinus (talk) 23:42, 3 December 2022 (UTC)
"thus, the Hosoya index" – I don't think this is a logical conclusion from the part preceding the semicolon, so I'd remove the thus Ovinus (talk) 04:57, 3 December 2022 (UTC)
Also what? The Hosoya index of a complete graph counts the number of patterns of pairwise connections between n vertices in a graph where any pair can be connected. The nth telephone number counts the number of patterns of pairwise connections between n subscribers to a telephone system where any pair can be connected. Except for changing the words "vertices" to "subscribers" and "graph" to "telephone system" they are exactly the same thing. The part before the semicolon explains why they are the same thing (because any pair can be connected). —David Eppstein (talk) 07:09, 3 December 2022 (UTC)
Oh, I see. I was reading it wrong, and thought "for which any pattern of pairwise connections is possible" was solely to describe complete graphs, rather than also as a logical tool for the connection to telephone numbers. Ovinus (talk) 19:11, 3 December 2022 (UTC)
Should it be "probabilist", "probabilistic" or "probabilist's"? I changed it to the latter but that's just my intuition. Ovinus (talk) 03:28, 4 December 2022 (UTC)
Should match the terminology in Hermite polynomial so I guess "probabilist's" is best. —David Eppstein (talk) 07:18, 4 December 2022 (UTC)
Few comments overall. I'll update you after tomorrow's ferment. Ovinus (talk) 03:28, 4 December 2022 (UTC)

Alright, happy with the article; good stuff. I suppose the few comments are commensurate with the article's length. Ovinus (talk) 03:12, 6 December 2022 (UTC)


#### Spotchecks
[1]: Don't have, sadly
The Art of Computer Programming is super low-level by modern computer science standards (everything is written in a made-up assembly language) but there's a lot of great material in there. I'd recommend it to anyone interested in computer science or computational mathematics. Also maybe second to Stanley as an essential reference for combinatorics. —David Eppstein (talk) 20:05, 4 December 2022 (UTC)
Indeed. I have the first volume, which shall be given company once I finish. Did you read it in school? Ovinus (talk) 20:54, 4 December 2022 (UTC)
I don't remember when I first read parts of it. I don't think I ever had (nor have given) a course that assigned it as official reading. —David Eppstein (talk) 21:39, 4 December 2022 (UTC)
[2]: Ditto
This one, on the other hand, is I think just a random combinatorics text, replaceable by any number of equivalent combinatorics texts. I don't have any complaints about it but I don't see it as standing out from a crowded field. —David Eppstein (talk) 20:08, 4 December 2022 (UTC)
[8]: Fine
[9]: Fine
[12]: Fine
[15]: Fine
[16]: Fine

Please check the first sentence:

the telephone numbers or the involution numbers are a sequence of integers...
Shouldn't be 'sequences' there?
-- (non-English speaker) CiaPan (talk) 07:34, 13 August 2022 (UTC)

There are many of these numbers, but only one sequence. But I changed the verb from "are" to "form" because the numbers and the sequence aren't really the same thing as each other. —David Eppstein (talk) 07:52, 13 August 2022 (UTC)