  We consider the representation theory of the Ariki-Koike algebra, a
$q$-deformation of the group algebra of the complex reflection group $C_r \wr
S_n$. We define the addition of a runner full of beads for the abacus display
of a multipartition and investigate some combinatorial properties of this
operation. We focus our attention on the $q$-decomposition numbers, i.e. the
polynomials arising from the Fock space representation of the quantum group
$U_q(\widehat{\mathfrak{sl}}_e)$. Using Fayers' LLT-type algorithm for
Ariki-Koike algebras, we relate $q$-decomposition numbers for different values
of $e$ for the class of $e$-multiregular multipartitions, by adding a full
runner of beads to each component of the abacus displays for the labelling
multipartitions.
