Semi-Pappus configurations; combinatorial generalizations of the Pappus configuration

Binomial partial Steiner triple systems with complete graphs: structural problems

“…and afterwards considering their 'product' {a, i 1 } ⊕ {i 1 , i 2 } and {a, i 1 } ⊕ {a ′ , i 2 } we see that, conversely, (iii) implies if a line L of M has two points common with H, two in (X \ A) ⊠ I or one in (X \ A) ⊠ I and the second in ℘ 2 (I) then L ⊂ H, and each line of M of the form (15) crosses H. (19) Finally, we pass to the lines of M of the form (16). Let p = {a 1 , a 2 } ∈ ℘ 2 (X), and b ∈ X, i ∈ I, q = {i, b}.…”