hypersimplex(d,k)

description

                 
 

	These polytopes are the convex hull of all of the vertices
	of a (0,1) d-cube whose coordinates sum to k. They 
	are a generalization of the simplex.

references

196, 121

keywords

zero-one

ambient_dim

                 
 
<p>
	d

equations

                 
 
<p>
	equality(k, ((-1) x d))

dim

d-1

n_vertices

choose(d,k)

n_facets

( k = = 1 || k = = d-1 ) ? d : 2d

vertices

	foreach $S (ksets($k,(1..$d))){
	   row(1,char_vec($d,@$S))
	}
	returnmatrix();