Cleanups and new features about corners and cells in partition and tableau

[sagetrac-numata]

The main goal of the patch was to add two functions namely arm_cells and leg_cells. On the way I found several bugs or inconsistencies:

Whereas the various cells methods returns the cells as tuple (i,j) Partition.corner used to return them as lists [i,j]. I changed them to return tuples. Various methods had to be fixed methods accordingly...

On the way I found that Tableaux.slide which uses Partition.Corner was modifying it's argument.

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: Partition cells arm legs

Author: Numata Yasuhide, Florent Hivert

Reviewer: Anne Schilling

Merged: sage-4.4.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/6655

[sagetrac-numata]

Attachment: trac_6655_partition_newfeature-ny.patch.gz

[hivert]

Changed keywords from Parition to Partition cells arm legs

[hivert]

Changed author from NUMATA Yaushide to NUMATA Yasuhide, Florent Hivert

[hivert]

comment:4

Should be ready for review ! Apply only trac_6655_partition_corner_cells-fh.patch

[hivert]

comment:5

I slightly improved the doc and re-uploaded the patch...

[hivert]

comment:6

I just discovered some failing docttests. Everything should now be ok. Please review

[anneschilling]

Reviewer: Anne Schilling

[anneschilling]

comment:7

Hi Florent,

Thank you for this patch. Here are a couple of comments:

• Please use consistently "in English convention" instead of "in english notations",
  see line 840, 963, 924.

• Would it be possible to lift the methods arm_length, leg_length, hook_length, arm_cells, etc also to SkewPartitions? I recently needed those and it would be convenient to have them directly in Sage.

Cheers,

Anne

[hivert]

Attachment: trac_6655_partition_corner_cells-fh.patch.gz

[hivert]

comment:8

• Please use consistently "in English convention" instead of "in english notations",
  see line 840, 963, 924.

Fixed...

• Would it be possible to lift the methods arm_length, leg_length, hook_length, arm_cells, etc also to SkewPartitions? I recently needed those and it would be convenient to have them directly in Sage.

Except for cells which I just added, they are all accessible through l.outer().arm_length... So I'm not sure we wan't to link all of those.

[anneschilling]

comment:9

Attachment: trac_6655_partition_corner_cells-review-as.patch.gz

I reviewed the patch. It cleans up several features in partitions. In addition it fixes the slide method in skew_tableaux and adds the cell method to skew_partitions as requested. All tests pass. Positive review!

Release manager, please apply only
trac_6655_partition_corner_cells-fh.patch and
trac_6655_partition_corner_cells-review-as.patch (in this order).

[sagetrac-mvngu]

comment:10

Merged in this order:

1. trac_6655_partition_corner_cells-fh.patch
2. trac_6655_partition_corner_cells-review-as.patch

[sagetrac-mvngu]

Changed author from NUMATA Yasuhide, Florent Hivert to Numata Yasuhide, Florent Hivert

[sagetrac-mvngu]

Merged: sage-4.4.2.alpha0