# Assignment polytope

### From Glossary

The assignment polytope is

The name originates from an interpretation of its extreme points in the
assignment problem. If
, assign person to task .
Each extreme point has the property that each element of is 0 or 1.
The sums describing the polytope require that each row () and each
column () has exactly one 1 in it. This means every person is assigned
to some task, and every task is assigned to be done by one person. The polytope
is also the set of doubly stochastic matrices, whose
extreme points are the *permutation matrices*.