Talk:Steiner system

Invention of designs

The indicated (published) sources refer to Woolhouse's problem as the invention of designs. The quotation is incorrect. The actual problem 1733 in the 1844 volume of Lady's and gentleman's diary is different, for it asks to “Determine the number of combinations that can be made out of n symbols, p symbols in each; with this limitation, that no combination of q symbols that may appear in any one of them shall be replicated in any other.” (With respect to the accepted definition of a design, some combinations of q symbols may be missing.)

Moreover, the solution of this problem is given in the 1845 volume of the Diary by Mr Septimus Bay, under the assumption that we have a true design, and he determines the number of blocks in a design with given parameters. A note indicate that such designs may or may not exist, depending on the chosen parameters. It is only later (Bose, Skolem,..., Keevash) that necessary and/or sufficient conditions have been given for the existence of designs. — Preceding unsigned comment added by 194.254.61.45 (talk) 14:39, 29 May 2019 (UTC)

The S(5,8,24)

Could someone tell why is it so "remarkable" ? Just telling that it's "connected" with something else it's really useful.

Well, the fact that it exists at all is remarkable. But to explain it fully would require an article on the Leech lattice and another on the sporadic simple groups (particularly the Mattieu groups, and the Conway groups, and the Monster). Some day, someone will probably write these. --Zundark, 2001 Dec 9

A late reply: there is Monster group. JDAWiseman (talk) 17:33, 3 September 2020 (UTC)

A short discussion or just a statement that there is a unique S(5,8,24) would be nice.

That's right. The discussion is way too technical. Zaslav 20:24, 27 February 2007 (UTC)

I expected there to be an article called "Witt design" for this. Shouldn't there at least be a redirect to this page? 170.140.150.23 (talk) 22:00, 21 November 2008 (UTC)

Kirkman's Schoolgirl Problem

Should it be included or should it have its own article?Mike92591 18:05, 29 August 2006 (UTC)

Separate article, IMO. It makes a nice historical story. Zaslav 20:22, 27 February 2007 (UTC)

Proof

The article says "As of 2012, an outstanding problem in design theory is if any nontrivial Steiner systems have t >= 6". It seems that Peter Keevash solved the problem: that for essentially all t, k, n, S(t, k, n) exists. [1] Sanxiyn (talk) 17:46, 25 February 2014 (UTC)

Also reported here. Deltahedron (talk) 18:00, 25 February 2014 (UTC)

My edit citing the preprint and based on the fact that the proof has been accepted by the relevant experts was reverted. I put it back. Do we need to have an edit war?

I have no intention to engage in an edit war over this. The result is spectacular, the technique admirable, but Wikipedia is not the place where new results are announced or praised. The preprint is a year and a half old, yet I can't find evidence that it has yet been published. It certainly stirred up a lot of blog activity, but that is not the same as the standard vetting process of a respected journal. Even after it is published it takes some time to get the result into the secondary sources, and it is only then that Wikipedia should incorporate the result - see WP:TOOSOON. Wile's first announcement of his result comes to mind (but this one is not nearly as complex as that one was) and should serve as a warning about rushing through the process. Bill Cherowitzo (talk) 19:02, 26 June 2015 (UTC)

Question on construction of S(5,8,24) from projective line

The group of linear broken transformations is isomorphic to PGL_2(23) with 12.144 elements and not to the special projective linear group PSL_2(23) which in fact has 6.072 elements as described. What is the argument to see why exactly 8 projective transformations in PSL_2(23) keep the initial block fix? Oyano Math (talk) 14:07, 14 November 2024 (UTC)