Combinatorics / CONCEPT

Two incidence counts and the codegree-four bound

Let H be a finite family of subsets of an n-element vertex type, m=card(H), and P=binom(n,2). The counts are defined for every H and include absent ground pairs; write hi=h(H,i) and qi=q(H,i). The cap means at most four neighbors per ground pair. Under the hypotheses stated below, fiber and incidence counts yield the bounds and exact correction identity.