Entropy and the Link Action in the Causal Set Path-Sum

In causal set theory the gravitational path integral is replaced by a path-sum over a sample space $Omega_n$ of $n$-element causal sets. The contribution from non-manifold-like orders dominates $Omega_n$ for large $n$ and therefore must be tamed by a suitable action in the low energy limit of the theory. We extend the work of Loomis and Carlip on the contribution of sub-dominant bilayer orders to the causal set path-sum and show that the link action suppresses the dominant Kleitman-Rothschild orders for the same range of parameters.