GAP (MatroidGeneration) - Chapter 1: Generate low-rank matroids

Compute the list of multiplicity vectors of rank 3 split matroids with n atoms. The function understands the Boolean option balanced and if true computes only balanced multiplicity vectors.

1.1-2 MinimalListOfCoatoms

Compute using the GAP package Images the minimal representative of the list of coatoms of the matroid on the atoms [ 1 .. n ].

1.1-3 Rank3MatroidIterator

Returns a recursive iterator riter of all rank 3 matroids with n atoms and given multiplicity vector mult_vec. The recursive iterator riter can for example be evaluated in hpcgap using

The function understands the Boolean option balanced and if true computes only balanced matroids.

#@if IsHPCGAP
gap> mult_vec := [ [ 2, 8 ], [ 3, 9 ], [ 5, 2 ] ];;
gap> riter := Rank3MatroidIterator( 11, mult_vec );
<iterator>
gap> state := rec( );;
gap> channel_of_matroids := CreateChannel(10^6);;
gap> ParallelyEvaluateRecursiveIterator( state, 8, riter, channel_of_matroids );
rec( shutdown := function(  ) ... end )
gap> coatoms1 := ReceiveChannel( channel_of_matroids );;
gap> coatoms1[1];
[ [ 1, 2, 3, 4, 5 ], [ 1, 6, 7, 8, 9 ], [ 1, 10, 11 ], [ 2, 6, 10 ],
  [ 2, 7, 11 ], [ 3, 6, 11 ], [ 3, 7, 10 ], [ 4, 8, 10 ], [ 4, 9, 11 ],
  [ 5, 8, 11 ], [ 5, 9, 10 ], [ 2, 8 ], [ 2, 9 ], [ 3, 8 ], [ 3, 9 ],
  [ 4, 6 ], [ 4, 7 ], [ 5, 6 ], [ 5, 7 ] ]
gap> coatoms2 := ReceiveChannel( channel_of_matroids );;
gap> coatoms2[1];
[ [ 1, 2, 3, 4, 5 ], [ 1, 6, 7, 8, 9 ], [ 1, 10, 11 ], [ 2, 6, 10 ],
  [ 2, 7, 11 ], [ 3, 6, 11 ], [ 3, 8, 10 ], [ 4, 7, 10 ], [ 4, 9, 11 ],
  [ 5, 8, 11 ], [ 5, 9, 10 ], [ 2, 8 ], [ 2, 9 ], [ 3, 7 ], [ 3, 9 ],
  [ 4, 6 ], [ 4, 8 ], [ 5, 6 ], [ 5, 7 ] ]
gap> ReceiveChannel( channel_of_matroids );
fail
#@fi

1 Generate low-rank matroids

1.1 Rank 3 matroids

1.1-1 GenerateMultiplicityVectorsOfRank3SplitMatroids

1.1-2 MinimalListOfCoatoms

1.1-3 Rank3MatroidIterator