In general,
transitivity is a property of a relation: if whenever a~b and b~c , then a~c , the relation is
transitive. Equality is a
transitive relation, so is (
set-wise)
containment.
In
group theory, when a
group has a
permutation action on a
set, the action is called
transitive if there are
group elements whose
permutation action is to exchange any given pair of
elements of the
set. Such an action is called
doubly-transitive if any two
ordered pairs can be exchanged by the
permutation action of some
group element,
triply-transitive if any two
ordered triples can be exchanged, etc.
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combinatorics--