Note

What's New:

### Sage Days 45 Coding Sprint Projects

This is the project page for Sage Days 45, and more generaly ICERM's semester on Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series.

Below is a list of proposed projects. You are welcome to add more projects or add yourself as participant for existing projects! The following feature request guidelines may help you specify useful and realistic project descriptions; if you are at ICERM, you are more than welcome to come discuss about those with the Sage fans there!

### Extended affine Weyl groups, affine Iwahori Hecke algebras, and nonsymmetric Macdonald polynomials

Dan Bump, Anne Schilling, Mark Shimozono, Nicolas Thiéry, Viviane Pons

See Trac Ticket 14102.

This project was started during Sage Days 40 by Dan Bump, Dan Orr, Anne Schilling, Mark Shimozono, and Nicolas Thiéry and preliminary patches are in the sage-combinat queue (see extended_affine_weyl_groups_sd40.patch and affine_iwahori_hecke_algebras.patch).

Viviane Pons: I have some programs already in sage-combinat on non symmetric Macdonald polynomials, see trac_6629_abstract_ring_of_multivariate_polynomials_with_several_bases_vp.patch

Viviane : patch is now on trac and ready to be reviewed !

### Finalization of the Coxeter3 integration into Sage

Anne Schilling, Nicolas Thiéry, Martina Lanini, Dan Bump

This would bring a faster implementation of Kazhdan-Lusztig polynomials to Sage.

See Trac Ticket 12912.

Status: - Anne : worked on 12912

### Finalization of Coxeter and Weyl groups patch

Mark Shimozono, Anne Schilling, Christian Stump

Finalization of the patch Trac Ticket 12774. Done!

Status: - Mark finalized patch and addressed reviewer concerns - Anne : reviewed Mark's patch -

### Further Kazdhan-Lusztig functionalities

Brant Jones, Chris Berg, Dan Bump

Status:

- Brant : - refactoring the current implementation to take advantage of WithRealizations - implemented KL basis for the Iwahori-Hecke algebra - implemented third basis for the algebra - not on trac yet, but will create a ticket ????

### Quantum Schubert products in general types (in particular type C) for the full flag variety

Liz Beazley

Approaches:

- Expose existing functionality from lrcalc: http://trac.sagemath.org/sage_trac/ticket/14107
- Sage rim-hook implementation (only as an interesting exercise, unless the implementation in lrcalc causes trouble)
- Puzzle rule (see below)
- From k-schur functions using substitution rule

### (Equivariant) puzzle rule

Liz Beazley, Anne Schilling, Allen Knutson, Franco Saliola

- Using Knuth's Dancing Links data structure: sage.combinat.matrices.dancing_links?
- Using hive model and counting of integer points in a polytope (Using Latte? or ?)

Status: - - Avinash : constructed Bellkale-Kumar puzzle pieces ; to be uploaded to sage-combinat

### Implementation of k-tableaux using alpha factorizations

Anne Schilling

### Review the root system plot ticket

Nicolas Borie, Nicolas Thiéry

### Review the affine ambient space patch

Mark Shimozono, Nicolas Thiéry

### Finalization of Denton's affine symmetric group patch

And possibly generic implementation of (affine) Coxeter groups as (affine) permutation groups, using (affine) permutations of the roots or the ambient space.

Chris Berg, Nicolas Thiéry

### Finalization of the partition options patch

Travis Scrimshaw and Andrew Mathas (and Nicolas)

Status: - Travis : finalized patch - Andrew : reviewing patch (almost done)

### Crystals and rigged configurations code and dependencies

Travis Scrimshaw, Anne

### Officially deprecate CombinatorialClass

I believe after #13605, there are only a few more left...

Travis Scrimshaw Vincent Delecroix

- Vincent : Reviewed one patch on compositions

### Split and finalize languages

Vincent Delecroix and Travis Scrimshaw

status : - Vincent : worked on pre-requisites. - Travis : reviewed Vincent's patch

### Posets

- adding functionality to poset elements--what does this mean?
- iterate over lattices
- zeta, order, characteristic polynomials

- characteristic polynomial done naively
- zeta polynomial from Stembridge's posets code
- W polynomial coming--relabel the poset and then look at permutations

- more examples of posets

- Young diagrams
- Semistandard tableaux
- interval posets

- graph_editor
- disjoint union, ordinal sum, product

Alex Csar, Kevin Dilks

- Status:
- Greene-Kleitman partition of posets (Darij) ; prototype algorithm ready, needs to be correctly formatted.
- Eric : poset avoidance (patch on trac 14099)
- Alejandro : fixing interface to graph colouring
- Kevin : first patch successfully uploaded to trac, now to post rest of code to trac

### Preparing technical details for Combinatorial Hopf Algebras

Main points are :

- Finalizing GradedEnumeratedSet
- Categories for Graded Connected Hopf Algebras With Basis (require point 1)
- Improve linear morphisms between GradedConnectedAlgebrasWithBasis (computation of matrices for each graded component, ...) (require point 2)
- Fix technical detail about composition of linear morphism

Nicolas Borie, Vincent Delecroix, Saliola

Status: - Vincent : finalized patch 10193 (under review; small things to fix) - Nicolas Borie : reviewing trac 10193 - Andrew : patch on indexed matrices trac 14103 - Nicolas Borie : tested Andrew's patch on indexed matrices trac 14103 - Nicolas Borie : patch for graded modules on the way

### Iterating through Partitions(n) for n>=1000

### Finalize more thematic tutorials and get them into Sage

- http://trac.sagemath.org/sage_trac/ticket/14090
- http://trac.sagemath.org/sage_trac/ticket/11490
- http://combinat.sagemath.org/doc/thematic_tutorials/index-sage-combinat.html
- Discuss the layout for exercises, ...

Nicolas Thiéry, Franco Saliola, ... We need proof readers!

### Cluster algebra package

3 tickets that need review/finalization

Gregg Musiker, Christian Stump, Salvatore

Status: - reviewed one patch (positive review) - almost done second patch (today!) - 3rd patch work in progress (to be finalized within a week)

### B infinity crystals

Ben, Mary Elisabeth, Travis

### General Coxeter groups

Christian, Richmond

### Digit sets

Finalization and review

Eva Curry

### Implementing (and optimizing) Sheicher and Thuswaldner algorithm for finding neighbors of an integral self-affine tile

(citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.4331&rep=rep1&type=pdf)

Eva

### Quasi symmetric functions / Combinatorial Hopf Algebras

Chris, Sara, Franco, Nicolas^2, Darij

Here is the worksheet from our first meetup on Tuesday evening

Here are some possible topics:

- QSym tutorial (see the Sym tutorial for inspiration ; use Sym tutorial as a pre-requiste)
- QSym documentation improvements : for instance, include "inject_shorthands"
- product_on_basis for the F-basis
- P-partition enumerators (Darij)
- chromatic quasi-symmetric functions (Alejandro, Eric)

- Status:
- P-partition enumerators (Darij) [.py files on trac, ready for review]
- Sara Billey : QSym tutorial (first draft ; ready for review)
- Sara Billey and Chris Berg : nicer documentation for inject_shorthands (essentially done)

### Quiver algebras and representations

Gregg?

### #11111: Finite dimensional vector spaces and algebras

Nicolas, Franco

### KLR-algebra

Gabe, Mathas, Mary Elizabeth, Travis

### Matrices indexed by whatever (and displayed as html)

Mathas, Nicolas

See Trac Ticket 14103 and Trac Ticket 14104.

### Generalized Specht modules

Sara, Alejandro, Darij, Chris, Franco

### Chromatic quasi-symmetric functions

### Number theory and automorphic forms

Hartmut, ...

### List to do for crystals from Crystal Session on Tuesday

- Plotting for Littelmann paths, performance check between Reda's and Mark/Anne's LS implementation (Reda, Mark, ...)
- B-infinity for finite types (Ben Salisbury, ...)
- MV polytopes (Mary, Dinakhar, ...)
- GLn action on crystals (Gautam, Anne, ...)

### Let's get to work and have fun!

Everybody

### Other projects

Arthur L : alcove paths working in all affine types ; visualizations working for type A ; and working through technicalities for other types

Findstat : - Viviane Pons is now the official web developer ; she got findstat working on her machine ! - Christian : new implementation is almost finished (Findstat-2.0 beta; available on github) - Chris Berg : adding new statistics - Sara Billey : adding new statistics

Trees : - (Viviane) patch for combinatorial maps between trees and other objects - patch almost ready for uploading to trac

Tutorials (presentations): - Chris Berg - Franco - Vincent - Nicolas - Viviane - Anne

Crystals: - Reda : plotting rank 2 crystals including latex output (for Littelmann Path model and tableaux) - Ben : finalized the implementation of generalized Young Walls (Anne and Travis reviewed the patch 14130)

Coxeter groups: - Ed Richmond : learning way around Sage ; started working on initial implementation of a class for arbitrary Coxeter groups

2+2==5: - Travis : created a patch so that Sage answers 5 to 2+2 (passes all doctests in integers and integer rings)

- Anne : finalized 14089, 14009, 14052
- Anne : reviewed 12774, 14130, 12912

Polynomials: - Travis : 14120 Laurent Polynomials - Travis : speed up of conversion of polynomials to finite fields 13257