Irredundant bases for the symmetric group

Abstract An irredundant base of a group acting faithfully on a finite set is a sequence of points in that produces a strictly descending chain of pointwise stabiliser subgroups in , terminating at the trivial subgroup. Suppose that is or acting primitively on , and that the point stabiliser is primitive in its natural action on points. We prove that the maximum size of an irredundant base of is , and in most cases . We also show that these bounds are best possible.