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M22 and Cameron graph constructors #14283
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comment:2
A much better way is to create these 77 blocks by applying the Mathieu group M_22 to one block, directly.
This is a bit unfortunate that one needs to write such an ugly call, instead of just PS. How does one find the block? Well, take the pointwise stabilizer of 3 points, say, 1, 2, 3 in |
comment:3
And with a minimum extra effort one may construct http://www.win.tue.nl/~aeb/graphs/Cameron.html using the same |
comment:4
Dimaaaaaaaaaaaaa... Please, give me one book to read so that I will know and understand all these things by myself and not stay helpless in front of your black magic ?.. Patch updated. Thank you very much ! Nathann |
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Changed author from Nathann Cohen to Nathann Cohen, Dmitrii Pasechnik |
Changed dependencies from 14271 to 14271, 14291 |
comment:7
Replying to @nathanncohen:
regarding Mathieu groups and Witt designs, there is e.g. a chapter "Three lectures on exceptional groups" in Conway & Sloan "Sphere Packings, Lattices and Groups". There are many more places where this stuff can be found, though. E.g. here: http://www.win.tue.nl/~aeb/2WF02/Witt.pdf By the way, there are more distance-transitive graphs which can be constructed from blocks of these designs. See [loc.cit.] and
Thanks for adding me in as a coauthor! a typo:
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comment:8
Updated ! And thank you for the references ! Nathann |
comment:10
a typo : |
comment:11
Updated ! Nathann |
comment:12
Now with an embedding. I recommend using Nathann |
comment:13
The doctests are failing : the Cameron graph does not seem to be correct |
comment:14
Replying to @fchapoton:
that's due to a bug or a feature in #14291 : the action |
Attachment: 14283_extra.patch.gz fix for Cameron graph |
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Reviewer: Dmitrii Pasechnik |
Work Issues: documentation |
comment:17
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comment:18
Arggggggggg... Sorry Fixed. Nathann |
comment:19
should be
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Changed work issues from documentation to none |
comment:20
Fixed too. |
Merged: sage-5.10.beta2 |
comment:21
Attachment: trac_14283.patch.gz |
Two other strongly regular graphs !
http://www.win.tue.nl/~aeb/graphs/M22.html
http://www.win.tue.nl/~aeb/graphs/Cameron.html
Nathann
apply
Depends on #14271
Depends on #14291
CC: @dimpase
Component: graph theory
Author: Nathann Cohen, Dmitrii Pasechnik
Reviewer: Dmitrii Pasechnik
Merged: sage-5.10.beta2
Issue created by migration from https://trac.sagemath.org/ticket/14283
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