The minimal size of a base for the Weyl group of the Cartan type. A base of a permutation group is a set $B$ such that the pointwise stabilizer of $B$ is trivial. For example, a base of the symmetric group on $n$ letters must contain all but one letter. Any base has at least $\log |G|/n$ elements, where $n$ is the degree of the group, i.e., the size of its domain.

The book thickness of a graph. The book thickness (or pagenumber, or stacknumber) of a graph is the minimal number of pages required for a book embedding of a graph.

The largest minimal number of arrows pointing to a cell in the Ferrers diagram in any assignment. Assign to each cell of the Ferrers diagram an arrow pointing north, east, south or west. Then compute for each cell the number of arrows pointing towards it, and take the minimum of those. This statistic is the maximal minimum that can be obtained by assigning arrows in any way.

The number of odd parts of a partition.

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 maximal multiplicity of an eigenvalue in a graph.

The multiplicity of the eigenvalue zero of the adjacency matrix of the graph.

The number of even parts of a partition.

The number of parts from which one can substract 2 and still get an integer partition.

The length of the border of a binary word. The border of a word is the longest word which is both a proper prefix and a proper suffix, including a possible empty border.