Opened 6 years ago
Closed 6 years ago
#14283 closed enhancement (fixed)
M22 and Cameron graph constructors
Reported by: | ncohen | Owned by: | tbd |
---|---|---|---|
Priority: | major | Milestone: | sage-5.10 |
Component: | graph theory | Keywords: | |
Cc: | dimpase | Merged in: | sage-5.10.beta2 |
Authors: | Nathann Cohen, Dmitrii Pasechnik | Reviewers: | Dmitrii Pasechnik |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #14271, #14291 | Stopgaps: |
Description (last modified by )
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
Attachments (2)
Change History (23)
comment:1 Changed 6 years ago by
- Component changed from PLEASE CHANGE to graph theory
- Status changed from new to needs_review
- Type changed from PLEASE CHANGE to enhancement
comment:2 Changed 6 years ago by
comment:3 Changed 6 years ago by
And with a minimum extra effort one may construct http://www.win.tue.nl/~aeb/graphs/Cameron.html using the same s=[...]
.
comment:4 follow-up: ↓ 7 Changed 6 years ago by
T_T
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 ?.. T_T
Patch updated. Thank you very much !
Nathann
comment:5 Changed 6 years ago by
- Description modified (diff)
- Summary changed from M22 graph constructor to M22 and Cameron graph constructors
comment:6 Changed 6 years ago by
- Dependencies changed from 14271 to 14271, 14291
comment:7 in reply to: ↑ 4 Changed 6 years ago by
Replying to ncohen:
T_T
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 ?..
T_T
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 the book `Distance-Regular Graphs' by Brouwer, Cohen and Neumaier (Springer, 1989).
Patch updated. Thank you very much !
Thanks for adding me in as a coauthor!
a typo:
1108 Returns the Cameon graph.
comment:8 Changed 6 years ago by
Updated ! And thank you for the references !
Nathann
comment:9 Changed 6 years ago by
- Dependencies changed from 14271, 14291 to #14271, #14291
comment:10 Changed 6 years ago by
a typo : unique strongly graph
comment:11 Changed 6 years ago by
Updated !
Nathann
comment:12 Changed 6 years ago by
Now with an embedding. I recommend using g.show(figsize=40)
:-P
Nathann
comment:13 follow-up: ↓ 14 Changed 6 years ago by
- Status changed from needs_review to needs_work
The doctests are failing : the Cameron graph does not seem to be correct
comment:14 in reply to: ↑ 13 Changed 6 years ago by
comment:15 Changed 6 years ago by
- Description modified (diff)
- Status changed from needs_work to positive_review
comment:16 Changed 6 years ago by
- Reviewers set to Dmitrii Pasechnik
comment:17 Changed 6 years ago by
- Status changed from positive_review to needs_work
- Work issues set to documentation
dochtml.log:[graphs ] /mazur/release/merger/sage-5.10.beta1/local/lib/python2.7/site-packages/sage/graphs/graph_generators.py:docstring of sage.graphs.graph_generators.GraphGenerators.CameronGraph:6: ERROR: Unknown target name: "http://www.win.tue.nl/~aeb/graphs/cameron.html". dochtml.log:[graphs ] /mazur/release/merger/sage-5.10.beta1/local/lib/python2.7/site-packages/sage/graphs/graph_generators.py:docstring of sage.graphs.graph_generators.GraphGenerators.M22Graph:6: ERROR: Unknown target name: "http://www.win.tue.nl/~aeb/graphs/m22.html".
comment:18 Changed 6 years ago by
- Status changed from needs_work to positive_review
Arggggggggg... Sorry :-/
Fixed.
Nathann
comment:19 Changed 6 years ago by
- Status changed from positive_review to needs_work
- Work issues documentation deleted
# long
should be
# long time
Changed 6 years ago by
comment:21 Changed 6 years ago by
- Merged in set to sage-5.10.beta2
- Resolution set to fixed
- Status changed from positive_review to closed
A much better way is to create these 77 blocks by applying the Mathieu group M_22 to one block, directly. Replace
s= [long long boring list]
byThis is a bit unfortunate that one needs to write such an ugly call, instead of just
MathieuGroup(22).orbit([1,2,3,7,10,20],"OnSets")
. IMHO it's worth opening a ticket and fixing this, i.e. adding"OnSets"
and other GAP options to the orbit method.PS. How does one find the block? Well, take the pointwise stabilizer of 3 points, say, 1, 2, 3 in
MathieuGroup(22)
and compute its orbits on the 22 points the group acts naturally. Such a stabilizer is the stabilizer of two points, 1 and 2, in the projective plane of order 4 induced on 2,3,...,22. There is unique like on 1 and 2 in this plane, so you'll see an orbit of length 3 that you need to add to 1, 2, 3 to get the block (this is the unique block on the 3 points 1, 2, 3).