Cardinalities of Irredundant Bases of Finite Primitive Groups

Abstract

Let [Formula: see text] be a finite permutation group acting on a set [Formula: see text]. An ordered sequence [Formula: see text] of elements of [Formula: see text] is an irredundant base for [Formula: see text] if the pointwise stabilizer of the sequence is trivial and no point is fixed by the stabilizer of its predecessors. We show that any interval of natural numbers can be realized as the set of cardinalities of irredundant bases for some finite primitive group.