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In this paper we characterize all nilpotent orbits under the action byconjugation that intersect the nilpotent centralizer of a nilpotent matrix $B$consisting of two Jordan blocks of the same size. We list all the possibleJordan canonical forms of the nilpotent matrices that commute with $B$ bycharacterizing the corresponding partitions.

Jordan structures of nilpotent matrices in the centralizer of a nilpotent matrix with two Jordan blocks of the same size