#9806: Constellations
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner: vdelecroix
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.2
Component: combinatorics | Resolution:
Keywords: constellation, | Merged in:
permutation, surfaces, graphs | Reviewers:
Authors: Vincent Delecroix | Work issues:
Report Upstream: N/A | Commit:
Branch: u/chapoton/9806 | be1b7b5b6803a2530ad13e0d0187c03d31cf91f1
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
I guess that it makes sense to move the remaining functions from
`sage.misc.permutation` inside `constellation.py`.
Since you are now using permutations, I would actually allow any domain.
In other words, add a fixed symmetric group attribute to `Constellations`.
When you check matching with the oeis sequence 220754, you can also do
that in Sage
{{{
sage: seq = oeis('A220754')
sage: seq
A220754: Number of ordered triples (a,b,c) of elements of the symmetric
group S_n such that the triple a,b,c generates a transitive group.
sage: seq.first_terms()
(1,
7,
194,
12858,
1647384,
361351560,
125116670160,
64439768489040,
47159227114392960,
47285264408385951360,
63057420721939066617600,
109118766834521171299756800,
239996135160204867851157273600,
659114500480471292127627441484800)
}}}
The fact that the associated permutation group is transitive is equivalent
to the "connectedness". You should either use one or the other.
--
Ticket URL: <http://trac.sagemath.org/ticket/9806#comment:62>
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