Talk:Telephone number (mathematics)

Question
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:
 * $$\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)

Ten digit telephone number
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)

+628
140.213.191.65 (talk) 21:50, 24 June 2021 (UTC)
 * Red question icon with gradient background.svg 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)

Plural/singular
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)