### Sage Days 40 Coding Sprint Projects

**For the main Sage Days 40 wiki page go** here.

Below is a list of proposed projects.

### Symmetric functions and Hopf algebras

#### Refactoring and extensions to symmetric functions / KSchur

Anne Schilling, Mike Zabrocki, Dorota

See also the review of Stembridge's packages below

#### Arithmetic dynamics & symmetric functions

Ben Hutz

#### Refactoring and extensions to Hopf algebras

Anne Schilling, Mike Zabrocki, John, Franco

#### Graded Algebras

Franco, John

#### Hopf algebras on graphs

Jeremy

#### NCSF/QSYM

Chris, Mike, Holly, Dorota, Franco, Nicolas?

#### Partition algebras and their reps

George

### Quiver representations

Gregg Musiker, Peter Webb, Franco Saliola, Charles Paquette, Alex Fink, Julie, Al Garver, Emily Gunawan

User stories:

### Clusters algebras from surfaces

Gregg Musiker, Al Garver, Weiwen Gu, Emily Gunawan

### Combinatorics

#### Alternating sign matrices

Jessica Striker

#### Graphs

Status as of Wednesday: Jeremy wrote some code to contract edges, check whether an edge is a cut-edge, and compute the Tutte polynomial. Lauren and Matt are beta-testing it. (It also needs commenting, examples, etc.)

Could you please poset the trac ticket number here? I am very interested to see your work (Anne).

Jeremy L. Martin, Anne Schilling, Tom, Lauren

- Tutte Polynomial

Kevin, Thomas

#### Review of what's missing from Stembridge's packages

Alex, Drew, Thomas, Kevin

#### Posets & Simplicial complexes

Demo including facade posets: Kim Vic

Jessica Striker, Jeremy, John^2, Charles?, Kevin, Thomas, Alex Csar?

Wish List:

- is_modular - Alex Csar
- is_atomic - Alex Csar
- is_semimodular - Alex Csar

- 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 - Kevin
- Semistandard tableaux - Jessica/Julie
- interval posets

- graph_editor
- disjoint union, ordinal sum, product
- make dual poset function work properly for lattices (it seems to break the join)

#### Simplicial Complexes:

Shellability

G-posets - homology modules

H_*(-, R), H^*(-, R) when R is neither **Z** nor a field

cup products trac #6102

cohomology operations

how to represent (co-)homology classes? trac #6100

links (already done)

stars

Cohen-Macaulay (trac #11523, needs review)

Fundamental Group (should not be too hard, using the code from trac #12339)

is_shifted

is_pseudo-manifold (trac #13226, needs review)

triangulate complex projective space (research problem; see mathoverflow)

chain complexes:

- fix bug for map induced by map of simplicial complexes: see trac #13220, positive review.
- induced map on homology (high priority) trac #6101
- mapping cone
- tensor product
- Tot of a bicomplex
- filtered chain complexes and the associated spectral sequence?

#### Topological structures & categories & their reps

Peter Webb, John

### Coxeter groups, Hecke algebras, Crystals, ...

#### Crystals

(trac #12251, positive review)

Anne Schilling, Mark Shimozono, Julie, Dan Bump, Ben Brubaker, Arthur Lubovsky

#### Extended Affine hecke algebras / weyl groups

Non symmetric Macdonald polynomials & friends in general types

Mark, Nicolas, Anne, Dan, Ben, Daniel

#### Integration of (affine) symmetric group and Coxeter groups

Alex Csar, Tom Denton, Holly

#### Complex reflexion groups

Alex Miller

#### Schubert Calculus

Mark, Alex, Nicolas, Kaisa, Yasuhide, Tom

#### Grothendieck polynomials / ...

Kaisa / Nicolas; checking out with Viviane's code Mark Shimozono, Jessica Striker

#### Statistics on permutations

Kim2

#### Matroids

Jeremy, Vic

I learned that there is a matroid project well underway already: see trac #7477 and/or the Google group sage-matroid. -- Jeremy

### Sage Documentation

John:

- build the documentation in parallel (trac #6495) needs review
- use MathJax by default when building the documentation (trac #13143) needs review

#### Sagetex

Nicolas, Dan

### Misc

#### Get my patches into Sage

Nicolas, Franco, Dan, Gregg

Anne (trac #12251, positive review), (trac #13224, positive review) (trac #13222, positive review)

### Interface to Gfan and version update

Marshall Hampton