# G

## General position

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.

## Generating Function

If *{a*_{0}, a_{1}, a_{2}, a_{3} ...} is a sequence of numbers,
it's generating function is the power series
*f(x) = a*_{0} + a_{1} x + a_{2} x^{2} +
a_{3} x^{3} ...

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

## Girth

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.

## Graph

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

## Group

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*.

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An On-line Dictionary of Combinatorics