Editing Matroid (section)

===Uniform matroids===
Let <math>E</math> be a finite set and <math>k</math> a [[natural number]]. One may define a matroid on <math>E</math> by taking every {{nobr|<math>k</math> element}} subset of <math>E</math> to be a basis. This is known as the ''[[uniform matroid]]'' of rank <math> k</math>. A uniform matroid with rank <math>k</math> and with <math>n</math> elements is denoted <math> U_{k,n}</math>. All uniform matroids of rank at least 2 are simple (see {{section link||Additional terms}}). The uniform matroid of rank&nbsp;2 on <math>n</math> points is called the <math>n</math>&nbsp;''point line''. A matroid is uniform if and only if it has no circuits of size less than one plus the rank of the matroid. The direct sums of uniform matroids are called [[partition matroid]]s.

In the uniform matroid <math> U_{0,n}</math>, every element is a loop (an element that does not belong to any independent set), and in the uniform matroid <math> U_{n,n}</math>, every element is a coloop (an element that belongs to all bases). The direct sum of matroids of these two types is a partition matroid in which every element is a loop or a coloop; it is called a ''discrete matroid''. An equivalent definition of a discrete matroid is a matroid in which every proper, non-empty subset of the ground set <math>E</math> is a separator.