Subquadrangle m-regular systems on generalized quadrangles
Antonio Cossidente, Tim Penttila · Journal of Combinatorial Designs · 2010
We introduce the notion of subquadrangle regular system of a generalized quadrangle. A subquadrangle regular system of order m on a generalized quadrangle of order (s, t) is a set ℛ of embedded subquadrangles with the property that every point lies on exactly m subquadrangles of ℛ. If m is one half of the total number of subquadrangles on a point, we call ℛ a subquadrangle hemisystem. We construct two infinite families of symplectic subquadrangle hemisystems of the Hermitian surface ℋ︁(3, q2), q odd, and two infinite families of symplectic subquadrangle hemisystems of 𝒲3(q2), q even. Some sporadic examples of symplectic subquadrangle regular systems of ℋ︁(3, q2) are also presented. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:28-41, 2010