The interval resolution global dimension of a poset. This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.

The number of even parts of a partition.

The number of distinct even parts of a partition. See Section 3.3.1 of [1].

The number of parts of a partition that are not congruent 0 modulo 3.

The number of induced stars on four vertices in a graph.

The minimal number of occurrences of the path-pattern in a linear ordering of the vertices of the graph. A graph is a disjoint union of paths if and only if in any linear ordering of its vertices, there are no three vertices $a < b < c$ such that $(a,c)$ is an edge. This statistic is the minimal number of occurrences of this pattern, in the set of all linear orderings of the vertices.

The minimal number of edges to add or remove to make a graph a line graph.

The number of doubly irreducible elements of a lattice. An element $d$ of a lattice $L$ is '''doubly irreducible''' if it is both join and meet irreducible. That means, $d$ is neither the least nor the greatest element of $L$ and if $d=x\vee y$ or $d=x\wedge y$, then $d\in\{x,y\}$ for all $x,y\in L$. In a finite lattice, the doubly irreducible elements are those which cover and are covered by a unique element.

The (zero)-forcing number of a graph. This is the minimal number of vertices initially coloured black, such that eventually all vertices of the graph are coloured black when using the following rule: when $u$ is a black vertex of $G$, and exactly one neighbour $v$ of $u$ is white, then colour $v$ black.

The minimum of the number of parts and the size of the first part of an integer partition. This is also an upper bound on the maximal number of non-attacking rooks that can be placed on the Ferrers board.