Integer partitions represent ways to write a positive integer as the sum of smaller positive integers, e.g., (2, 2, 1) is a partition of n = 2 + 2 + 1 = 5. Brylawski showed that for a fixed n∈ℕ these partitions can be ordered by dominance, under which they become a complete lattice 𝓛ₙ. A classic result of Hardy and Ramanujan shows that the sequence of sizes (|𝓛ₙ|)ₙ∈ℕ, which is A000041 in Sloane’s On-line Encyclopedia of Integer Sequences, grows asymptotically as exp(π√ ̅2̅n̅/̅3̅ )/(4√ ̅3̅n̅ ). The increasingly more complicated lattices 𝓛ₙ can be described more compactly by their so-called standard contexts (𝓙(𝓛ₙ), 𝓜(𝓛ₙ), ≤), where 𝓙(𝓛ₙ) denotes the set of completely join-irreducible and 𝓜(𝓛ₙ) the set of completely meet-irreducible elements of 𝓛ₙ. In the talk we discuss how so-called arrow relations between 𝓙(𝓛ₙ) and 𝓜(𝓛ₙ) can be used to obtain subdirectly irreducible factors for subdirect representations of 𝓛ₙ, and we present descriptions of these arrow relations for all n∈ℕ.