Let us say that cyclic boolean function is a function such that we can connect all its True vertices with edges (in boolean cube) and get a cycle. Let the number of edges in this cycle equals $n$. I need to find the number of irreducible DNFs (disjunctive normal forms) for the cyclic boolean function with cycle length n (maybe asymptotically).
I've already have a solution of the problem connected to that: for snake boolean function (such that all its True vertices connected with edges generate a chain of length $n$) there are asymptotically $c \cdot \lambda^n$ irreducible DNFs where $c$ is a constant and $\lambda$ is the a real root of equation $x^3 - x - 1 = 0$. Moreover, it is said that for cyclic function I will have the same asymptotic but another constant $c$.
Can you please help me to find the solution?