Notion of descent/major index in tableau.py is not mathematically standard

[jbandlow]

The 'descents' and 'major_index' methods of a Tableau return what are more properly known as 'i_descents' and the 'i_maj' statistic. These should be renamed accordingly, and the proper statistics put in their place. See, eg., Richard Stanley--Enumerative Combinatorics, Vol. 2 for a reference to the usual definition.

EDIT by Darij:

Apply:

• attachment: trac_7983-major_index_and_other_tableau_fixes-dg.patch
• attachment: trac_7983-review-ts.patch

Depends on #8392

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

Component: combinatorics

Keywords: combinat, tableaux, days49

Author: Amarpreet Rattan, Darij Grinberg

Reviewer: Jason Bandlow, Travis Scrimshaw

Merged: sage-5.12.beta0

Issue created by migration from https://trac.sagemath.org/ticket/7983

[sagetrac-arattan]

comment:1

I have made a patch that resolves this issue.

What I have done is renamed the old methods 'major_index' and 'descents' to 'i_major_index' and 'i_descents'. From what I can tell, only one other method refers to either of these methods and that is 'inversion', and I have not changed that at all except to refer to the new 'i_descents' (in particular I have not changed the name of 'inversion').

I have then made new methods called 'major_index' and 'descents' which use a more standard definition (i.e. the one on pages 361 and 363 of Enumerative Combinatorics Vol 2 by R. Stanley).

[sagetrac-arattan]

Reviewer: jbandlow

[sagetrac-arattan]

patch to fix tableaux major index

[jbandlow]

comment:2

Attachment: Fix_Tableau_Major_Index_AR.patch.gz

Thanks for the patch! While I don't have time for a full review now, the main issue with this patch is going to be backward compatibility. I'm pretty sure that the Macdonald polynomial code uses these functions, so sage --testall will probably fail after applying your patch. That part will not be too hard to fix, but the bigger problem is for people who have sage code on their own machine. When people upgrade sage and this change is included (without them necessarily knowing about it) this change could make their code behave in slightly wrong ways that are not obvious. We really try to avoid that.

So I think the thing to do is to deprecate 'descents' and 'major_index' (look up deprecation in the developers guide), use 'i_descents' and 'i_major_index' for the existing statistics (as you have done) and give the classical statistics some new name. (Suggestions welcome!)

[sagetrac-arattan]

comment:3

Replying to @jbandlow:

Thanks for the patch! While I don't have time for a full review now, the main issue with this patch is going to be backward compatibility. I'm pretty sure that the Macdonald polynomial code uses these functions, so sage --testall will probably fail after applying your patch. That part will not be too hard to fix, but the bigger problem is for people who have sage code on their own machine. When people upgrade sage and this change is included (without them necessarily knowing about it) this change could make their code behave in slightly wrong ways that are not obvious. We really try to avoid that.

So I think the thing to do is to deprecate 'descents' and 'major_index' (look up deprecation in the developers guide), use 'i_descents' and 'i_major_index' for the existing statistics (as you have done) and give the classical statistics some new name. (Suggestions welcome!)

Yes, I thought this would be an issue. I actually made the patch a while ago but thought that precisely your objection would be raised. Anyways, I decided to send it in and see what would happen. It sounds like you have a good solution.

About a new name: is "Major_Index" a bad idea? I don't know about sage's naming conventions.

[darijgr]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 The 'descents' and 'major_index' methods of a Tableau return what are more properly known as 'i_descents' and the 'i_maj' statistic.  These should be renamed accordingly, and the proper statistics put in their place.  See, eg., Richard Stanley--Enumerative Combinatorics, Vol. 2 for a reference to the usual definition.
+
+*Apply: [attachment: trac_7983-major_index_and_other_tableau_fixes-dg.patch]

[darijgr]

Changed keywords from none to combinat, tableaux