#14808: Permutation([1,2,3,5,4]).recoils_composition() returns [5] instead of
[4,
1], and similar bugs
-----------------------------+----------------------------------------------
Reporter: darij | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: PLEASE CHANGE | Keywords: combinat, permutations
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Darij Grinberg
Merged in: | Dependencies:
Stopgaps: |
-----------------------------+----------------------------------------------
{{{
sage: Permutation([1,2,3,5,4]).descents_composition()
[4, 1]
sage: Permutation([1,2,3,5,4]).recoils_composition()
[5]
}}}
This just has to be wrong. The recoils composition of a permutation is the
descent composition of its inverse; in particular, a self-inverse
permutation such as {{{[1,2,3,5,4]}}} should have the two compositions
equal.
I think the main problem is that the actual recoils composition has its
descent set formed by the values of the recoils, not the positions of the
recoils. I'm fixing this in the attached patch. (This entails changing the
doctest. But even with if the recoils composition would be computed using
the positions rather than the values, that doctest would have been wrong.)
Wrong as well:
{{{
sage: Permutation([1,2,3]).recoils_composition()
[]
}}}
Also, {{{recoils_composition}}} should return an actual {{{Composition}}},
not just a list.
And here is my favorite permutation once again:
{{{
sage: Permutation([]).descents_composition()
[0]
}}}
{{{[0]}}} is not a composition.
Nothing bad about Mathworld references, but they shouldn't replace a
definition, particularly if the definition given in Mathworld is confusing
( http://mathworld.wolfram.com/PermutationRun.html ).
Attached is a fix to these issues. I'm not very happy with it because the
old version of {{{recoils_composition}}} (once properly corrected) might
have been a more interesting map than the true recoils composition -- but
I can't find any reference to it under that name in literature.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14808>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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