The number of join-irreducible elements of a lattice. An element $j$ of a lattice $L$ is '''join irreducible''' if it is not the least element and if $j=x\vee y$, then $j\in\{x,y\}$ for all $x,y\in L$.

The number of elements in the poset.

The number of indecomposable injective modules with projective dimension at most one in the incidence algebra of the poset.

The largest nonnegative integer which is not a part and is smaller than the largest part of the partition.

The largest part of an integer partition.

The maximal part of the shifted composition of an integer partition. A partition $\lambda = (\lambda_1,\ldots,\lambda_k)$ is shifted into a composition by adding $i-1$ to the $i$-th part. The statistic is then $\operatorname{max}_i\{ \lambda_i + i - 1 \}$. See also [[St000380]].

The maximum of the length and the largest part of the integer partition. This is the side length of the smallest square the Ferrers diagram of the partition fits into. It is also the minimal number of colours required to colour the cells of the Ferrers diagram such that no two cells in a column or in a row have the same colour, see [1]. See also [[St001214]].