Subquadrangle m-regular systems on generalized quadrangles

✍ Scribed by Antonio Cossidente; Tim Penttila

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 153 KB
• Volume: 19
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20260

✦ Synopsis

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 H(3, q 2 ), q odd, and two infinite families of symplectic subquadrangle hemisystems of W 3 (q 2 ), q even. Some sporadic examples of symplectic subquadrangle regular systems of H(3, q 2 ) are also presented. q 2010