Originally Posted by
xliioper
Domestic FC fares are dual inventory fares (they start with coach fare class letters in fare basis codes). There must be inventory in both FC fare bucket corresponding to booking class of fare, and the underlying coach fare bucket for the fare (first letter of fare basis code). Z booking class FC fares use L/U/T/X/V coach basis classes and you can see there are a couple of flights with no L/U/T/X/V inventory on Jan 1. I booking class FC fares use Q and K fare basis classes.
BE and C+ fares are also dual inventory fares (BE fares have single E booking class, while C+ use W and S booking class).
I don't argue with your premise the vast majority of the time, but trust me, if coach is sold out and F has inventory, there is a First Class fare that can be sold that does not require a mated coach inventory to be available. It may be $3k, but there is a true first class fare published.