A matroid flat is a subset 
of the underlying set 
of a matroid such that adjoining
any element outside 
increases its matroid rank. Writing 
for the matroid rank function,
the condition is
 |
Equivalently, 
is maximal among subsets having its matroid
rank.
For a matroid represented by the columns of a matrix, a flat consists of all column labels whose columns belong to a specified subspace spanned by columns of the matrix. The number of flats of each matroid rank is the subject of Mason's conjecture on flats.
