Counting Necklaces

A necklace is an

m

-coloring of the vertices of a regular

n

-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

n

-bead necklaces for

n=3

through

n=35

. Several examples are provided to clarify the notation used and illustrate necklaces fixed by rotation or reflection.