## Open Problems in Representing State Spaces for Cultural Transmission Models

### Seriation Graphs

#### How large is the space of Laplacian spectra on unlabelled trees with N vertices?

Cayley’s theorem tells us the number of possible unlabelled trees on \(N\) vertices: \(n^{n-2}\). This can be very large (e.g., for \(n=20\), around \(10^{23}\)). But the number of distinguishable Laplacian spectra may be much smaller. It is worth understanding how large this state space of spectra may be for different numbers of assemblages.

#### Is there a useful notion of the “spectrum” of a time varying graph?

### References Cited