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GKMVarieties :: FlagMatroid

FlagMatroid -- the class of all flag matroids


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


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.

See also

Functions and methods returning a flag matroid :

Methods that use a flag matroid :

For the programmer

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