A generalised quadrangle is a point–line incidence geometry G such that: (i) any two points lie on at most one line, and (ii) given line L point p not incident with L, there unique collinear p. They are specific case of the polygons introduced by Tits (1959), these structures their automorphism groups some importance in finite geometry. An integral part understanding quadrangles knowing which c...
We construct examples and families of locally Hermitian ovoids the generalized quadrangle $$H(3,q^2)$$ . also obtain a computer classification all for $$q \le 4$$ , compare obtained $$q=3$$ with H(3, 9) which is by computer.
For n > 3, every n×n partial Cayley matrix with at most n−1 holes can be reconstructed by quadrangle criterion. Moreover, the holes can be filled in given order. Without additional assumptions, this is the best possible result. Reconstruction of other types of multiplication tables is discussed.
We give a new proof of the theorem of Joszéf Dénes: If L1 and L2 are distinct latin squares of order n ≥ 2, n / ∈ {4, 6}, that satisfy the quadrangle criterion, then L1 and L2 differ in at least 2n entries.
