Semi Laguerre i-structures

Abstract

AbstractA Dembowski semi-plane is a semi-plane obtained from a projective plane by Dembowski's method [1]. A semi Laguerre i-structure i ⩾ 1, is an incidence structure J = (P, B1 ∪ B2, I) for which: (i) each element of P is incident with one element of B1, (ii) an element of B1 and an element of B2 are incident with at most one common element of P, (iii) each i-residual space of J (with respect to B1) is a Dembowski semi-plane, (iv) B2 ≠ Ø and each element of B2 is incident with at least i elements of P. In [4] we determined all semi Laguerre 1-structures. Now we determine all semi Laguerre i-structures, i ⩾ 2