We rederive Manolescu’s unoriented skein exact triangle for knot Floer homology over combinatorially using grid diagrams, and extend it to the case with coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, we reestablish the homological –thinness of quasialternating links.
"Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology." Algebr. Geom. Topol. 17 (3) 1283 - 1321, 2017. https://doi.org/10.2140/agt.2017.17.1283