An association scheme intersection number is a constant 
attached to three relations 
, 
, and 
of an association scheme
or coherent configuration. It is the number
of elements 
such that 
and 
, where 
is any member of 
. The defining axioms require this number to be independent
of the particular pair 
.
The intersection numbers are the structure constants for multiplication in the Bose-Mesner algebra or, more generally, the adjacency algebra of a coherent configuration.
