Bender-Knuth involutions and standardization of semistandard Young tableaux

[darijgr]

I've implemented standardization and Bender-Knuth involutions on straight and skew semistandard tableaux. I've also fixed two typos in error strings and copied some methods for straight tableaux into the skew tableaux file (though I believe much more should be done in this direction).

EDIT: Finished, thanks to Travis.

Apply:

• attachment: trac_14574-folded.patch

CC: @tscrim

Component: combinatorics

Keywords: tableaux, partitions, combinat

Author: Darij Grinberg

Reviewer: Travis Scrimshaw

Merged: sage-5.10.beta5

Issue created by migration from https://trac.sagemath.org/ticket/14574

[darijgr]

Attachment: trac_14574_preliminary_version.patch.gz

not yet merge ready

[darijgr]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 Here is a **preliminary** patch; I will look at it with a fresh mind tomorrow and maybe catch a few bugs, as well as add the same functionality to skew semistandard tableaux. (I guess I should then replace the code in tableau.py by more or less a reference to the code in skew_tableau.py?)
+
+I have also fixed two typos in error strings. Now that might theoretically cause a doctest avalanche, but hell it was necessary.

[darijgr]

Attachment: trac_14574-bender_knuth_et_al-v1.patch.gz

[darijgr]

Attachment: trac_14574-bender_knuth_et_al-v1.2.patch.gz

Finished version -- please review

[darijgr]

Description changed:

--- 
+++ 
@@ -1,3 +1,4 @@
-Here is a **preliminary** patch; I will look at it with a fresh mind tomorrow and maybe catch a few bugs, as well as add the same functionality to skew semistandard tableaux. (I guess I should then replace the code in tableau.py by more or less a reference to the code in skew_tableau.py?)
+I've implemented standardization and Bender-Knuth involutions on straight and skew semistandard tableaux. I've also fixed two typos in error strings and copied some methods for straight tableaux into the skew tableaux file (though I believe much more should be done in this direction).
 
-I have also fixed two typos in error strings. Now that might theoretically cause a doctest avalanche, but hell it was necessary.
+Apply:
+* [attachment: trac_14574-bender_knuth_et_al-v1.patch](https://github.com/sagemath/sage-prod/files/10657779/trac_14574-bender_knuth_et_al-v1.patch.gz)

[darijgr]

comment:3

[trac_14574-bender_knuth_et_al-v1.2.patch] and [trac_14574-bender_knuth_et_al-v1.patch] are the same file; I derped again when uploading.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:4

Hey Darij,

I've made some changes in my review patch to the implementations. In particular, here's a comparison of my implementation of the Bender-Knuth inversions. Here's mine:

sage: T = SemistandardTableaux(shape=[6,3,3,1], max_entry=5)
sage: T.cardinality()
4000
sage: %time L = [x.bender_knuth_involution(2) for x in T]
CPU times: user 4.49 s, sys: 0.21 s, total: 4.70 s
Wall time: 4.94 s

Yours:

sage: %time L = [x.bender_knuth_involution(2) for x in T]
CPU times: user 4.78 s, sys: 0.11 s, total: 4.88 s
Wall time: 5.16 s

So there's not much difference, but I'd guess mine could be shown (eventually) to be slightly faster on larger sets. Anyways, if you agree with my changes, you can set this to positive review.

Thanks,

Travis

PS - For future reference, you'll need your real name in the authors section.

[tscrim]

Changed author from darij to Darij Grinberg