I was reading this paper, and came across an equation which gives an expression for the number of necklaces of beads in two colors, with length n. $Z_n = \dfrac{1}{n} \displaystyle \sum \limits_{d \mid n} \phi \left( d \right) 2^{n/d}$ The author says that this equality is well known, and cites Golomb and Riordan as […]

I’ve read that one can use the Polya enumeration theorem or the Burnside’s lemma to count the number of necklaces using $n$ beads from $k$ colors. Can we then find a way to count the number of necklaces such that no adjacent beads are of the same color?

Intereting Posts

Can sets of cardinality $\aleph_1$ have nonzero measure?
Energy for the 1D Heat Equation
Blackboard bold, Bold, Fraktur, and Reserved Variable.
Ellipse with non-orthogonal minor and major axes?
Unique matrix of zeros and ones
Combinatorial proof involving partitions and generating functions
How to choose a proper contour for a contour integral?
Is it possible that the zeroes of a polynomial form an infinite field?
Intuition behind the definition of Adjoint functors
Monte-Carlo simulation with sampling from uniform distribution
Where is the order of the variables inside the parentheses coming from?
Any two groups of three elements are isomorphic – Fraleigh p. 47 4.25(b)
Element-wise (or pointwise) operations notation?
Find the degree of the splitting field of $x^4 + 1$ over $\mathbb{Q}$
The strong topology on $U(\mathcal H)$ is metrisable