How close to ready is sage for teaching undergrad/grad combinatorial courses

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Textbooks:

Brualdi - Introductory Combinatorics

Wilf - Zeilberger Generating functionalogy

Stanley - Enumerative Combinatorics

CAGES Combinatorial http://www.math.mtu.edu/~kreher/cages.html

Knuth Graham Pataschnik - Concrete mathematics

van Lint, Wilson: A course in Combinatorics http://www.amazon.com/Course-Combinatorics-J-van-Lint/dp/0521422604

Graphs:

• - Complete, except maybe chromatic number and Hamiltonian paths? - interface with graphviz: There is some functionality to interface NetworkX with graphviz and some algorithms that are implemented directly in Cython (like spring layout). We also have a way to interface with pygraphviz, but it's probably not as natural or as easy as it should be.

  - See CombinatoricaCompare for a comparison to the fairly comprehensive graph theory functionality of the Mathematica Combinatorica package.

Trees:

• - spanning trees / ... are there
  • maybe they should return a Graph (could be made to return graph by creating an empty graph and adding the returned edges).
  - no specific data structure for trees (orderered, ...)
  • Parts could be taken from MuPAD-Combinat
  - basic decomposable objects / species

Posets:

• - TODO: (integrate Stembridge + MuPAD-Combinat)

Linear programming:

• - Should be there ... - Networks?

Coding theory:

• - Link with Guava in GAP: sage.coding.guava

Automata

• - There exist specialized things in pyrex

Classical combinatorial objects

• - Should be complete enough: partitions / ...

Generating functions

• - guess / ... (TODO: port Martin Rubey's implementation in Axiom)