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 numbers of flats of each matroid rank are the Whitney numbers of the second kind. Their proposed logarithmic concavity is the subject of Mason's conjecture on flats.
