... x)−z. By multisection of series, the generating function G(x, y) for our present problem isG(x, y) =P (x, y, 1)2−P (x, y, −1)2. The first term on the right is half the generating function ... 1). (5.3) By (e), or by (c) if k = 1, we see that this is strictly negative if 1 <α<k+1. Sinceck+1(α) is continuous, it is strictly decreasing for 1 <α<k+ 1. By continuity and (a),positivity ... labels for the rest of the structureand(c) replacing i by ai in D where [n] \ S = {a1<a2< }.At first, deciding the truth or falsity of (i) in a particular instance may seem trivial....