I'm working on the consistency of Martin's axiom and I need some help counting. Assume we are in a universe where GCH holds and $\kappa$ is a regular cardinal. How many non-isomorphic partial orders are there of size less than $\kappa$. I think the answer is $\kappa$ (indeed this is what Jech writes) and can convince myself, but it is not very clear to me how to systematically count the number of different partial orders of a certain size.
Let me know if I need to give more context, I'm asking my specific question in a general way.