#12278: misleading (outdated) docstring in partitions_restricted
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Reporter: AlexGhitza | Owner: sage-combinat
Type: defect | Status: new
Priority: minor | Milestone: sage-5.4
Component: combinatorics | Resolution:
Keywords: partitions docstring | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by andrew.mathas):
Here is another related example which I think is incorrect:
{{{
sage: Partitions(4,min_slope=-2).list()
[[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]
}}}
In sage (and in mathematics)
{{{
sage: Partition([4]) == Partition([4,0])
True
}}}
so the partition `[4]` does not satisfy the constraint min_slope=-2.
In modular representation theory, a partition is said to be
**e-restricted** if the difference of its successive parts is always
strictly less than `e`, for an integer `e>1`. The partitions index the
irreducible representations of the Iwahori-Hecke algebra of the symmetric
group at a primitive `e`th root of unity.
If `min_slope` worked the way that I expected it to then `Partitions(m,
min_slope=1-e)` would construct the `e`-restricted partitions of n.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12278#comment:5>
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