Various improvements to the implementation of Fomin's growth diagrams

[mantepse]

Implement the backward rule for Sylvester insertion on binary trees, and make the dual graded graphs accessible.

Also allow for multiple edges in the dual graded graphs, implement shifted insertion and affine insertion as examples.

CC: @sagetrac-sage-combinat @tscrim @anneschilling @nthiery @darijgr

Component: combinatorics

Author: Martin Rubey, Travis Scrimshaw

Branch/Commit: 43b6324

Reviewer: Martin Rubey, Travis Scrimshaw, Darij Grinberg

Issue created by migration from https://trac.sagemath.org/ticket/23319

[mantepse]

Branch: u/mantepse/growth_diagram_improvements

[mantepse]

Author: Martin Rubey

[mantepse]

Commit: bf1d772

[mantepse]

New commits:

bf1d772

add backward rule for Sylvester, add access to the graded graphs

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6c34a9c	micro improvement to the backward rule in GrowthDiagramBinWord
74260a3	add support for multiple edges, add class for shifted shapes

[sagetrac-git]

Changed commit from bf1d772 to 74260a3

[sagetrac-git]

Changed commit from 74260a3 to 2785f3f

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2785f3f

fix P_chain and Q_chain for graphs with multiple edges, record disagreement in ShiftedShapes

[sagetrac-git]

Changed commit from 2785f3f to 53d37c7

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

53d37c7

lazy import shifted shapes, fix forward rule, fix tests

[mantepse]

comment:7

There are still some missing doctests to make the patchbot happy, which I'll provide in time, but it should be functional.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

e96e3e1

fix missing DiGraph import

[sagetrac-git]

Changed commit from 53d37c7 to e96e3e1

[sagetrac-git]

Changed commit from e96e3e1 to f1ba932

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f1ba932

add backwards rules for shifted shapes

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5a66779

initial version of a class for LLMS insertion

[sagetrac-git]

Changed commit from f1ba932 to 5a66779

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

cc4110c

almost done with LLMS insertion

[sagetrac-git]

Changed commit from 5a66779 to cc4110c

[sagetrac-git]

Changed commit from cc4110c to 8853225

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8853225

fix a bug and add more (failing) tests

[sagetrac-git]

Changed commit from 8853225 to 995d6d6

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

995d6d6

fix final fehler, produce P_symbol as StrongTableau

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

3ed851b

A little bit more of doc polish.

[tscrim]

Reviewer: Martin Rubey, Travis Scrimshaw

[tscrim]

comment:105

I've done a few more changes and somewhat foregoing comment:87 and comment:90 to have a mix of both ways in the module-level documentation (which is primarily for new users) in the spirit of just completing this. If my changes are good, then go ahead and set this to a positive review.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c2ed8d3

fix a parenthesis, remark on duality, fix _check_duality, add test

[sagetrac-git]

Changed commit from 3ed851b to c2ed8d3

[mantepse]

comment:107

I was implementing a pair of dual graphs, and had a bug. To make debugging easier, I made the message in _check_duality better. To do so, I also had to be consistent with "up in P and down in Q". To understand that, I added a remark on duality.

Apart from that, I removed a parenthesis.

If it's OK, please go ahead and set it to positive (finally :-)

If you dislike the more verbose error message, you can remove it, modify it, whatever you like!

[darijgr]

comment:108

Is the singular in "its predecessor" really intended? As in, there is only one?

[sagetrac-git]

Changed commit from c2ed8d3 to 28ddfbe

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

28ddfbe

no, it's not a tree

[mantepse]

comment:110

slightly embarrassed :-)

[tscrim]

comment:111

One last little typo:

assigning to each vertex the formal sum of its predecessor,

should be predecessors. Once done, you can set a positive review on my behalf.

[tscrim]

Changed reviewer from Martin Rubey, Travis Scrimshaw to Martin Rubey, Travis Scrimshaw, Darij Grinberg

[mantepse]

comment:112

Wonderful!

I have yet another example ready - although without forward and backward rule because I don't know them: Dual graded graphs for (skew) quasisymmetric Schur functions. https://arxiv.org/pdf/1512.04614v1.pdf.

I have the graphs, and the conversion from a saturated chain in the P-graph to a CompositionTableaux.

Could you please confirm that it's better to put this in another ticket?

Or should I push?

[tscrim]

comment:113

I would say another ticket since this one is big enough already.

[sagetrac-git]

Changed commit from 28ddfbe to 43b6324

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

43b6324

fix typos, add reference

[mantepse]

comment:116

Yippee!

[tscrim]

comment:117

Thank you for all of your work on this.

[mantepse]

comment:118

Follow up on #23941 :-)

[vbraun]

Changed branch from public/combinat/improve_growth_diagrams-23319 to 43b6324