We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knows in the standard contact ℝ3 and Eliashberg and Hofer's contact homology. We use this translation to transport the idea of "coherent orientations" from the contact homology world to Chekanov's combinatorial setting. As a result, we obtain a lifting of Chekanov's differential graded algebra invariant to an algebra over ℤ[t,t-1] with a full ℤ grading.
"Invariants of Legendrian Knots and Coherent Orientations." J. Symplectic Geom. 1 (2) 321 - 367, June, 2002.