Weights of multipartitions and representations of Ariki–Koike algebras

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A Survey of Multipartitions Congruences and Identities (2008, background): “[13], [16]), some with applications to physics [12], we see multipartitions playing an important auxiliary role.”
Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A (2009, background): “If ℓ > 1 then def β coincides with Fayers [18] definition of weight for the algebras H Λβ .”
Representation theory of symmetric groups and related Hecke algebras (2009, unknown): “Let us take “ < ” to be any total ordering on Pµ,λ satisfying the following two conditions: (1) If (ν, κ), (θ, ϕ) ∈ Pµ,λ, then ν θ implies (ν, κ) < (θ, ϕ); (2) If (ν, κ), (ν, ϕ) ∈ Pµ,λ, then κ ϕ implies (ν, κ) < (ν, ϕ).”
BLOCKS OF CYCLOTOMIC HECKE ALGEBRAS (2006, methodology): “needed to show that our two equivalence relations on the set of multipartitions coincide when q 6= 1 and when the parameters Q1,...,Qr are non–zero. Here we are greatly aided by recent work of Fayers [14,15] on the ‘core block’ of a multipartition. Finally, in section 4 we consider the blocks of the”