# Stuttering multipartitions and blocks of Ariki–Koike algebras

### Résumé

There is a natural shift action deﬁned on multipartitions and their associated multisets of residues. Two diﬀerent multipartitions may have the same associated residues multiset, thus the orbit cardinality of a multipartition is always greater than or equal to the orbit cardinality of the associated residues multiset. Conversely, a given residues multiset is always associated to a multipartition with the same orbit cardinality. Using the abacus representation of a partition, we will see how the proof reduces to an integer quadratic optimisation problem

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Università degli Studi di Milano Biccoca, Milan (Italie)
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