General runner removal and the Mullineux map

We prove a new `runner removal theorem’ for $q$-decomposition numbers of the level 1 Fock space of type $A_{e-1}^{(1)}$, generalising earlier theorems of James–Mathas and the author. By combining this with another theorem relating to the Mullineux map, we show that the problem of finding all $q$-decomposition numbers indexed by partitions of a given weight is a finite computation.