#12643: irreducibility of generalized permutation
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Reporter: vdelecroix | Owner:
vdelecroix
Type: defect | Status:
needs_review
Priority: major | Milestone:
sage-5.1
Component: combinatorics | Resolution:
Keywords: permutation, quadratic differentials | Work issues:
Report Upstream: N/A | Reviewers:
Authors: vdelecroix | Merged in:
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
> but I would prefer if I can be just slightly more serious.
Me too ;-)
> Is there an easy place where I can try to understand the meaning of
>
> iet.GeneralizedPermutation('a a b','b c c') ?
>
> or
>
> GP('1 2 3 4 5 1','5 6 6 4 3 2')
You have to think as the standard two lines notation for permutations. For
example, the permutation
{{{
p(1) = 2, p(2) = 1, p(3) = 3
}}}
would be denoted
{{{
1 2 3
2 1 3
}}}
Then iet.Permutation('1 2 3', '2 1 3') is just a version of the
permutation above. But we are interested in the so called interval
exchange transformations (see Figure 1 p. 8 of [BL]) and it is better to
have two order of labels instead of a permutation. The object
iet.Permutation is two lines of symbols where each symbol appears once in
the first line and once in the second.
Generalized Permutations encode the combinatorics of more complicated maps
called linear involution (see Figure 6 p 16 of [BL]). The object
iet.GeneralizedPermutation is two lines of symbols where each symbol
appear twice.
.. [BL] Boissy-Lanneau http://arxiv.org/abs/0710.5614
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12643#comment:6>
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