Implement Bases of NCSF and QSym

[sagetrac-chrisjamesberg]

This patch is an attempt to implement new bases of NCSF and QSym which currently exist on the combinat server. This includes the Monomial basis and Fundamental basis of Tevlin, the dual of the quasisymmetric Schur function introduced by Haglund, Luoto, Mason and van-Willigenburg, the Immaculate basis, introduced by Berg, Bergeron, Saliola, Serrano and Zabrocki. In QSym, it will implement all of the dual bases of NCSF.

Currently the attached patch implements only the Quasisymmetric Schur functions of Haglund, Luoto, Mason, and van-Willigenburg, plus some combinatorics of Composition Tableaux

---

Apply:

• attachment: trac_13505_quasi_schur.5.patch

Depends on #14101

CC: @saliola @sagetrac-sage-combinat

Component: combinatorics

Keywords: NCSF QSym

Author: Chris Berg, Jeffrey Ferreira

Reviewer: Travis Scrimshaw

Merged: sage-5.12.beta5

Issue created by migration from https://trac.sagemath.org/ticket/13505

[sagetrac-chrisjamesberg]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
-This patch is an attempt to implement new bases of NCSF and QSym which currently exist on the combinat server. This includes the Monomial basis , Fundamental, dual of Qsym schur, Immaculate, Pieri Schur
+This patch is an attempt to implement new bases of NCSF and QSym which currently exist on the combinat server. This includes the Monomial basis and Fundamental basis of Tevlin, the dual of the quasisymmetric Schur function introduced by Haglund, Luoto, Mason and van-Willigenburg, the Immaculate basis, introduced by Berg, Bergeron, Saliola, Serrano and Zabrocki.
 
-Qsym Schur, Complete, Psidual, immaculate dual, Phidual, Forgotten, 
+In QSym, it will implement all of the dual bases of NCSF.

[jeffpferreira]

comment:3

Chris,

Are you still working on this? I see the patches on the combinat server but don't see a patch here on trac for the quasisymmetric Schur functions. If you'd like to provide a patch of what you have I am happy to review it, add to it, finish it, or whatever.

-Jeff

[jeffpferreira]

Attachment: trac_13505_quasi_schur.patch.gz

Applies cleanly to sage-5.10.rc1

[jeffpferreira]

Changed author from Chris Berg to Chris Berg, Jeffrey Ferreira

[jeffpferreira]

comment:4

I uploaded a patch which implements composition tableaux and quasi symmetric Schur functions. The majority of the code is from the combinat patch Chris mentions in the ticket description, except I changed the class of CompositionTableau to more closely follow sage/combinat/tableau.py. I have also included a backtracker to help speed up iter methods.

I am working on doc strings and doing more tests of the patch, but thought it worthwhile to post the current state considering FPSAC starts next week in Pairs.

-Jeff

[jeffpferreira]

Attachment: trac_13505_quasi_schur.2.patch.gz

Apply to 5.10

[jeffpferreira]

comment:5

Uploaded a new patch. Fixed a few edge-case bugs. Doc strings are next. I'll leave as 'needs_work' until I can get those done.