  We investigate the standard context, denoted by
$\mathbb{K}\left(\mathcal{L}_{n}\right)$, of the lattice $\mathcal{L}_{n}$ of
partitions of a positive integer $n$ under the dominance order. Motivated by
the discrete dynamical model to study integer partitions by Latapy and Duong
Phan and by the characterization of the supremum and (infimum) irreducible
partitions of $n$ by Brylawski, we show how to construct the join-irreducible
elements of $\mathcal{L}_{n+1}$ from $\mathcal{L}_{n}$. We employ this
construction to count the number of join-irreducible elements of
$\mathcal{L}_{n}$, and show that the number of objects (and attributes) of
$\mathbb{K}\left(\mathcal{L}_{n}\right)$ has order $\Theta(n^2)$.
