FlagMatroid -- the class of all flag matroids

Description

A flag matroid $\mathbf M$ is an ordered list $\{M_1, \ldots, M_k\}$ of Matroids on a common ground set such that $M_i$ is a matroid quotient of $M_{i+1}$ for all $i=1, \ldots, k-1$. The matroids $M_i$'s are called the "constituent" matroids of the flag matroid $\mathbf M$. The class FlagMatroid is a HashTable with two keys:

groundSet, whose value is a Set representing the common ground set of the constituent matroids
constituents, whose value is a List of Matroids

Caveat

Flag matroids are the first examples beyond ordinary matroids of a more general combinatorial family known as Coxeter matroids. Coxeter matroids have not been implemented yet.

Functions and methods returning a flag matroid :

flagMatroid(List) -- see flagMatroid -- construct a flag matroid
flagMatroid(Matrix,List) -- see flagMatroid -- construct a flag matroid

Methods that use a flag matroid :

bases(FlagMatroid) -- compute the bases of a flag matroid
flagGeomTuttePolynomial(FlagMatroid) -- see flagGeomTuttePolynomial -- computes the flag-geometric Tutte polynomial of flag matroids
isWellDefined(FlagMatroid) -- check if a flag matroid is well-defined
latticePoints(FlagMatroid) -- lattice points of a base polytope of a flag matroid
makeKClass(GKMVariety,FlagMatroid) -- the equivariant K-class of a flag matroid

For the programmer

The object FlagMatroid is a type, with ancestor classes HashTable < Thing.