Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

# Glossary

## Bijection

The identification of a "one-to-one" correspondence--enables us to enumerate a set that may be difficult to count in terms of another set that is more easily counted.

## Complete Graph

A graph in which every node is connected to every other node is called a complete graph.

## De Bruijn Sequence

A de Bruijn sequence is the shortest string that contains all possible permutations of a particular length from a given set.

## Hamilton Cycle

A Hamilton cycle is a path that visits every node in a graph and ends where it began.

## Permutation

An arrangement where order matters.

## Pigeonhole Principle

Of central importance in Ramsey Theory, and in combinatorics in general, is the "pigeonhole principle," also known as Dirichlet's box. This principle simply states that we cannot fit n+1 pigeons into n pigeonholes in such a way that only one pigeon is placed in each hole, with no pigeons left over.

## Ramsey Theory

Ramsey Theory reveals why we tend to find structure in seemingly random sets. Ramsey numbers indicate how big a set must be to guarantee the existence of certain minimal structures.