# Cyclotomic identity

In

mathematics, the

**cyclotomic identity** states that

where

*M* is

Moreau's necklace-counting function

and μ is the classic Möbius function of number theory. The denominator on the right, 1 −

*z*^{ j}, is a

cyclotomic polynomial -- hence the name.

## Reference

Nicholas Metropolis & Gian-Carlo Rota. *The Cyclotomic Identity.* Reprinted in *Gian-Carlo Rota on Combinatorics*. Birkhäuser. Boston. 1995.