Open Problems in Representing State Spaces for Cultural Transmission Models

 Created: 21 Jun 2020 Modified: 23 Jul 2020 BibTeX Entry RIS Citation Print

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.