Identifying Partitions with maximum commuting orbit $Q=(u,u-r)$

The authors here show that the partition $P_{k,l}(Q)$ in the table $\mathcal{T}(Q)$ of partitions having maximal nilpotent commutator a given stable partition $Q$, defined in [IKVZ2], is identical to the analogous partition $P_{k,l}^Q$ defined by the authors in [BIK] using the Burge correspondence.