Macaulay2 » Documentation
Packages » GKMVarieties :: FlagMatroid
next | previous | forward | backward | up | index | toc

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.

See also

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:

For the programmer

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


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/GKMVarieties/Documentation_GKMVarieties.m2:1823:0.