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GKMVarieties :: isWellDefined(FlagMatroid)

isWellDefined(FlagMatroid) -- check if a flag matroid is well-defined

Synopsis

Description

A FlagMatroid with constituent matroids $\{M_1, \ldots, M_k\}$ is well-defined if $M_i$ is a matroid quotient of $M_{i+1}$ (i.e. every flat of $M_i$ is a flat of $M_{i+1}$) for all $i = 1, \ldots, k-1$.

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

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

o1 : FlagMatroid
i2 : isWellDefined FM

o2 = true
i3 : FMbad = flagMatroid {uniformMatroid(2,4), uniformMatroid(1,2)++uniformMatroid(2,2)}

o3 = a flag matroid with rank sequence {2, 3} on 4 elements 

o3 : FlagMatroid
i4 : isWellDefined FMbad

o4 = false

See also