Matroids
Results
Select matroids and click an operation above.
Creates U(n,r): all r-subsets of {1,…,n} are bases.
Notation: ne(d, r; Y1|…|Yk; r1,…,rk)
d = ground set size, r = rank.
Layers = Yi, the new elements added at step i
(Xi = Xi−1 ∪ Yi, X0 = ∅). One layer per line, comma-separated.
Together the layers must cover {1,…,n}.
Rank bounds = ri, the rank of Xi. Strictly increasing; last value = r.
Example: layers 1,2 / 3,4, bounds 1,2
→ ne(4, 2; {1,2}|{3,4}; 1,2) with X1={1,2}, X2={1,2,3,4}.
sh({1,…,n}, A): B = {b₁<…<bᵣ} is a basis iff bᵢ ≤ aᵢ for all i.
Click on empty space to add a vertex.
Drag from one vertex to another to add an edge.
Right-click a vertex or edge to delete it.
Columns are the ground set {1,…,n}. Bases = maximal linearly independent column sets (over ℝ).
Ground sets are relabelled automatically so they are disjoint.