A coherent configuration on a finite set 
is a partition 
, 
, ..., 
of 
such that the diagonal is a union of relations, the
transpose of every relation is another relation, and, whenever 
, the number
 |
depends only on 
,
,
and 
.
The constants 
are the intersection numbers of the configuration.
A coherent configuration is homogeneous when the diagonal itself is one relation; homogeneous coherent configurations are association
schemes. A coherent configuration is Schurian when its relations are the orbits
on ordered pairs of a permutation group acting
on 
.
