Abstract
Polya's Counting Theory
Polya's counting theory provides a method to count configurations where certain
symmetry operations reduce the total number. For example, if you want to count
the number of essentially distinct necklaces that can be made from 20 red beads
and 20 blue beads, you need to notice that since the necklace is circular and could
be flipped over, any patterns that differ simply by being a rotation or reflection of
the necklace should be considered the same. Polya's technique uses the structure
of the symmetry permutations to give an almost magical expression with which many
such counting problems can be solved.