def show_partition_types(n,k):
G = []
Cn = graphs.CycleGraph(n)
for edges in combinations_iterator(filter(lambda (x,y): abs(x-y) % (n-1) > 1, combinations_iterator(range(n), 2)), k):
g = Cn.copy()
g.add_edges(edges)
G.append(g)
def dimension_of_span(n, k):
dim_counts = {}
for rays in combinations_iterator(all_ray_matrices(n), k):
kers = [r.image() for r in rays]
dim = reduce(lambda x,y: x.intersection(y), kers).dimension()
dim_counts[dim] = dim_counts.get(dim,0) + 1
return dim_counts
