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GKMVarieties :: bases(FlagMatroid)

bases(FlagMatroid) -- compute the bases of a flag matroid

Synopsis

Description

An ordered list $\{B_1, \ldots, B_k\}$ of sets is a basis of a flag matroid $\mathbf M = \{M_1, \ldots, M_k\}$ if $B_i$ is a basis of $M_i$ and $B_i \subseteq B_{i+1}$ for all $i$. This method computes the bases of a flag matroid.

i1 : FM = flagMatroid {uniformMatroid(2,4),uniformMatroid(3,4)}

o1 = a flag matroid with rank sequence {2, 3} on 4 elements 

o1 : FlagMatroid
i2 : bases FM

o2 = {{set {0, 1}, set {0, 1, 2}}, {set {0, 1}, set {0, 1, 3}}, {set {0, 2},
     ------------------------------------------------------------------------
     set {0, 2, 3}}, {set {0, 2}, set {0, 1, 2}}, {set {1, 2}, set {1, 2,
     ------------------------------------------------------------------------
     3}}, {set {1, 2}, set {0, 1, 2}}, {set {0, 3}, set {0, 2, 3}}, {set {0,
     ------------------------------------------------------------------------
     3}, set {0, 1, 3}}, {set {1, 3}, set {1, 2, 3}}, {set {1, 3}, set {0, 1,
     ------------------------------------------------------------------------
     3}}, {set {2, 3}, set {0, 2, 3}}, {set {2, 3}, set {1, 2, 3}}}

o2 : List

See also