The number of distinct squares in a binary word. A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uu$ is a factor of the word. Note that every word of length at least four contains a square.

The degree of symmetry of a binary word. For a binary word $w$ of length $n$, this is the number of positions $i\leq n/2$ such that $w_i = w_{n+1-i}$.

The metric dimension of a graph. This is the length of the shortest vector of vertices, such that every vertex is uniquely determined by the vector of distances from these vertices.

The arboricity of a graph. This is the minimum number of forests that covers all edges of the graph.

The balance of a binary word. The balance of a word is the smallest number $q$ such that the word is $q$-balanced [1]. A binary word $w$ is $q$-balanced if for any two factors $u$, $v$ of $w$ of the same length, the difference between the number of ones in $u$ and $v$ is at most $q$.

Half the length of a longest factor which is its own reverse-complement of a binary word.

The maximal modular displacement of a permutation. This is $\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation $\pi$ of $\{1,\dots,n\}$.

The Colin de Verdière graph invariant.

The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.

The dimension of a graph. The dimension of a graph is the least integer $n$ such that there exists a representation of the graph in the Euclidean space of dimension $n$ with all vertices distinct and all edges having unit length. Edges are allowed to intersect, however.