Another character theoretic formula for base size.

A base for a permutation group G acting on a set Ω is a sequence B of points of Ω such that the pointwise stabiliser G B is trivial. The base size of G is the size of a smallest base for G. Extending the results of a recent paper of the author, we prove a 2013 conjecture of Fritzsche, Külshammer, and Reiche. Moreover, we generalise this conjecture and derive an alternative character theoretic formula for the base size of a certain class of permutation groups. As a consequence of our work, a third formula for the base size of the symmetric group of degree n acting on the subsets of { 1 , 2 , ⋯ , n } is obtained.