Stuttering multipartitions and blocks of Ariki–Koike algebras


There is a natural shift action defined on multipartitions and residue multisets of their Young diagrams. Two multipartitions with the same residue multiset may have different orbit cardinalities, but the orbit cardinality of a given residue multiset is the maximum of the orbit cardinalities of all associated multipartitions. Using the abacus representation of a partition, we will see how the proof reduces to a quadratic integer minimisation problem.

CIRM, Luminy