Number of weighted vacuum Feynman diagrams

[th13]

I didn't know where to put this, because it isn't a homework or coursework I have to do but just a thing I'm trying to understand. Anyway, I have attached the problem as an image.

We have a scalar quartic lagrangian in d dimensions. It says that the number of vacuum Feynman diagrams, at a given order λ^k, weighted by their statistical factor, should depend on the number of dimension d.
If understand well what the "statistical factor" is, i.e. the number of ways to join the vertices of a given diagram, I can't figure out how it could be dependent on the number of space-time dimensions d. Any suggestions?

Thank you and sorry for my English

 

[Nate810]

! The statistical factor is the number of ways to arrange the edges of a given graph. This includes factors such as symmetry, which can affect the number of ways a graph can be arranged. In the context of a scalar quartic lagrangian in d dimensions, the number of vacuum Feynman diagrams at a given order λ^k will depend on the number of space-time dimensions d because the number of ways to arrange a diagram is dependent on the number of available edges. For example, if d=2, then there would be fewer edges available to arrange the vertices of a graph than if d=3 or higher. This means that the number of ways to arrange the vertices of a graph would be lower in two dimensions than in three or higher dimensions.