Throughout the library's documentation readers will find the following symbols:

• \(n\) to denote the number of vertices in a graph,
• \(s,t,u,v\) to typically denote vertices of a graph; we may use other letters,
• \(m\) to denote the number of edges in a graph,
• \(\pi\) to denote a linear arrangement, and \(\pi_I\) to denote the identity arrangement,
• \(T\), \(G\) to denote (usually) a tree or a more general graph,
• \(Q(G)\) to denote the set of pairs of independent edges of a graph \(G\),
• \(D(G)\) or \(D_\pi(G)\) to denote the sum of length of edges of a graph \(G\) arranged with \(\pi\).
• \(C(G)\) or \(C_\pi(G)\) to denote the number of edge crossings of a graph \(G\) arranged with \(\pi\).
• \(\langle k^x \rangle\) to denote the sum of degrees of the vertices of a graph raised to the power \(x\) averaged by \(n\).

For statistical properties of random variables, we usually use

• \(\mathbb{E}\) to denote expected value, and
• \(\mathbb{V}\) to denote variance.

For conditioned expected values and variances we use subindices, such as

• \(\mathrm{pr}\) to denote that the probability space is conditioned to the space of projective linear arrangements; \(\mathbb{E}_{\mathrm{pr}}\)
• \(\mathrm{pl}\) to denote that the probability space is conditioned to the space of planar linear arrangements; \(\mathbb{E}_{\mathrm{pl}}\).