  We generalize an inequality conjectured by Pohst in 1977 and recently proved
by the author and independently by Battistoni and Molteni. This new inequality
improves a bound for the regulator in terms of the discriminant for totally
real number fields by taking into account the signs of conjugates of the
fundamental unit. We give a new interpretation to the problem and exploit the
combinatorial method used by Pohst.
