On the Non-Existence of a Class of Configurations Which Are Nearly Generalized n-Gons

Abstract It is known [10] that if P is a v × v(n, s, s)-configuration with n ⩾ 3 and s ⩾ 2, then v ⩾ v0 ≡ 1 + s + s2 + … + sn−1, with strict inequality holding unless n = 3, 4, or 6. In this paper conditions on n and s are found which imply v ≠ v0 + 1. Indeed, we conjecture that equality can hold only when n = 3 and s = 2 or s = 3.