An orbital of a permutation group 
acting on a finite set 
is a group
orbit of the componentwise group action of 
on the Cartesian
product 
.
Thus the orbital containing 
is
 |
The paired orbital of 
is 
.
An orbital is self-paired if it equals its
paired orbital, so 
.
The diagonal orbital 
is also called the trivial orbital
when the action is transitive. More generally, the diagonal is a union of orbitals,
one for each group orbit of 
on 
.
An orbital is the arc set of an orbital digraph. A nondiagonal self-paired orbital, or a nondiagonal orbital together with its paired orbital, gives the edge set of an undirected orbital graph.
