Rotational invariance of quadromer correlations on the hexagonal lattice

In 1963 Fisher and Stephenson (Phys. Rev. (2) 132 (1963) 1411) conjectured that the monomer-monomer correlation on the square lattice is rotationally invariant. In this paper we prove a closely related statement on the hexagonal lattice. Namely, we consider correlations of two quadromers (four-vertex subgraphs consisting of a monomer and its three neighbors) and show that they are rotationally invariant.