#10630: Add a multi-partition implementation to sage
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Reporter: pabryan | Owner: pabryan
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.0
Component: combinatorics | Keywords: multipartition multi-partition
multi-partite multipartite partition
Work_issues: | Upstream: N/A
Reviewer: | Author: Paul Bryan
Merged: | Dependencies:
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Comment(by ebriand):
Some comments:
* The functions for multipartitions do not seem to work correctly. Here
is an incorrect (incomplete) result:
{{{
M=MultiPartitions([2,2])
for x in M.list(): print x
[[2, 2]]
[[1, 2], [1, 0]]
[[2, 1], [0, 1]]
[[1, 0], [1, 0], [0, 2]]
[[1, 1], [1, 0], [0, 1]]
[[2, 0], [0, 1], [0, 1]]
[[1, 0], [1, 0], [0, 1], [0, 1]]
}}}
Two multipartitions are missed: `[[1,1],[1,1]]` and `[[2,0],[0,2]]`
* I wonder whether `MultiPartitions` is a good name, because it seems it
has a different meaning in a near context. See for instance this paper by
G. Andrews: http://es.scribd.com/doc/6625886/Multi-Partitions, or this
other paper; http://www.maths.qmul.ac.uk/~mf/papers/weight2.pdf, or these
slides: http://www.cs.clemson.edu/~goddard/MINI/2009/Swisher.pdf ."Vector
partitions" may be safer (it is used for instance by George Andrews in his
book on partitions).
* Should one represent the Multipartitions as lists of vectors with
integer coordinates rather than lists of lists ? (because sometimes one
has to do the sum of the parts).
* A few typos:
* Line 6 of the file: "the" should not be repeated.
* Line 9 of the file: replace "it's" with "its".
* Line 63 of the file: replace "lexicographically order integer lists"
with "lexicographically weakly decreasing lists of integers" or something
better.
* Also, one might replace the definition of multipartition as
"equivalence class of tuples" (lines 4 to 10) with "multiset of tuples".
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10630#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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