We observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar–Wang to the description of the contact invariant due to Honda–Kazez–Matić. We include an example of this combinatorial calculation.
"A combinatorial description of the Heegaard Floer contact invariant." Algebr. Geom. Topol. 7 (3) 1201 - 1209, 2007. https://doi.org/10.2140/agt.2007.7.1201