flats(ZZ,Arrangement) -- list the flats of an arrangement of a given rank

Synopsis

• Function: flats

• Usage:

  flats(n,A)

• Inputs:
  • n, an integer, rank
  • A, a hyperplane arrangement, hyperplane arrangement
• Outputs:
  • a list, a list of flats of rank $n$

Description

i1 : A = typeA(3)

o1 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
       1    2   1    3   1    4   2    3   2    4   3    4

o1 : Hyperplane Arrangement 

i2 : flats(2,A)

o2 = {{3, 4, 5}, {1, 2, 5}, {0, 5}, {0, 2, 4}, {1, 4}, {2, 3}, {0, 1, 3}}

o2 : List

i3 : flats A

o3 = {{{}}, {{5}, {4}, {3}, {2}, {1}, {0}}, {{3, 4, 5}, {1, 2, 5}, {0, 5},
     ------------------------------------------------------------------------
     {0, 2, 4}, {1, 4}, {2, 3}, {0, 1, 3}}, {{0, 1, 2, 3, 4, 5}}}

o3 : List

See also

• circuits(CentralArrangement) -- list the circuits of an arrangement
• flats(Matroid) -- flats of a matroid