In R^3 with its standard contact structure there are two ``classical" invariants of Legendrian knots known as the rotation number, and the Thurston-Bennequin number. Possible values for the classical invariants are restricted by the underlying topological knot type. For instance, within a fixed topological knot type an upper bound for the Thurston-Bennequin number can be distilled from the Kauffman polynomial. Fuchs conjectured that this upper bound should be sharp precisely when the front diagram of a Legendrian knot admits a special type of decomposition known as a normal ruling. In this talk, I will describe a confirmation of Fuchs' conjecture which gives a combinatorial interpretation for certain coefficients of the Kauffman (and also the HOMFLY) polynomial in terms of normal rulings. Normal rulings play a role in other aspects of Legendrian knot theory, and, time permitting, I may survey relationships with the Legendrian contact homology invariant introduced by Chekanov and Eliashberg or with generating families.