G

A problem instance is said to be in general position if certain algebraic coincidences (depending on the problem at hand) do not occur. For point sets in R^d, this usually means that no k points are on a (k-2)-flat.

If {a₀, a₁, a₂, a₃ ...} is a sequence of numbers, it's generating function is the power series f(x) = a₀ + a₁ x + a₂ x² + a₃ x³ ...

For instance the generating function for the sequence {1,2,3,4...} is (1-x)^-2

The girth of a graph is the length of the smallest cycle in the graph that doesn't repeat vertices. The tetrahedron is girth 3, the cube and K(3,3) are girth four, the Petersen graph is girth 5.

A set N of nodes, together with a multi-set E of pairs of nodes called edges.

A group G consists of a set of elements together with a (one) binary associative operation subject to the following additional constraints:

• There is an identity element e such that ex = xe = x is true for all x in G.
• For each x in G there is an inverse element y such that yx=xy=e.