#9806: Constellations
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Reporter: vdelecroix | Owner:
Type: enhancement | vdelecroix
Priority: major | Status:
Component: combinatorics | needs_work
Keywords: constellation, permutation, | Milestone:
surfaces, graphs | sage-5.11
Authors: vdelecroix | Resolution:
Report Upstream: N/A | Merged in:
Branch: | Reviewers:
Stopgaps: | Work issues:
| documentation
| Dependencies:
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Comment (by vdelecroix):
Thanks for your corrections.
`perms_canonical_labels` is a way to conjugate a tuple of permutations
(s_1,s_2,\ldots,s_k) in such way that two conjugate tuples have the same
image under this canonical labeling. The reason is that (as in topological
graph) we want to consider isomorphism class of objects. Though, in
Graph/DiGraph the method is simply named `relabel` and perhaps I should
stick to this convention. One advantage here is that this method is very
fast (complexity O(n^2) for a tuple of degree n).
I am starting to use intinsively the patch. And the most interesting part
is not yet in there: I am interested in the set of constellations with
fixed profile (or passport). In other words, I want to fix the conjugacy
classes of all permutations. There is no such parent in the current patch.
Note that generating constellations of fixed profile is far less trivial
than generating constellations. . We have at least one interesting thing:
we know the cardinality of that set via representation theory (Frobenius
formula). But I do not know how much the formula is praticable (there is a
sum over all characters of the group).
--
Ticket URL: <http://trac.sagemath.org/ticket/9806#comment:28>
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