Uniform Matroid

discrete-mathematics combinatorics

Definition

Uniform Matroid

A matroid over an -element ground set is a uniform matroid if the family of independent sets is

for some constant . A subset is independent exactly when its size is at most .

Example

Let and . Then

Every subset of size at most is independent; the subsets of size and are dependent. The bases are exactly the six -element subsets, so the rank is .