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

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

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

Sagetex

Nicolas, Dan

Get my patches into Sage

Nicolas, Franco, Dan, Gregg

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