Arrow relations in lattices of integer partitions

We give a complete characterisation of the single and double arrow relations of the standard context K(Ln) of the lattice Ln of partitions of any positive integer n under the dominance order, thereby addressing an open question of Ganter, 2020/2022. •Type D partitions allow up-arrows, which fail to be down-arrows, to all types I–IV.•Type IV partitions allow down-arrows, which fail to be up-arrows, to all types A–D.•Type D partitions have double arrows only to those of type IV and vice versa.•Partitions of types A–C are double arrow related only to types I–III and vice versa.•For n≥3 there are exactly 2n−4 one-generated arrow-closed (1×1)-subcontexts of K(Ln).