# Counting Necklaces

Counting Necklaces

A necklace is an -coloring of the vertices of a regular -gon. The vertices are interpreted as the beads of the necklace. This Demonstration shows the computations involved in using Burnside's lemma to count the number of -bead necklaces for through . Several examples are provided to clarify the notation used and illustrate necklaces fixed by rotation or reflection.

m

n

n

n=3

n=35