Let S be a generalized quadrangle of order (q 2,q) containing a subquadrangle S′ of order (q,q). Then any line of S either meets S′ in q+1 points or is disjoint from S′. After Penttila and Williford (J. Comb. Theory, Ser. A 118:502–509, 2011), we call a subset H of the lines disjoint from S′ a relative hemisystem of S with respect to S′, provided that for each point x of S∖S′, exactly half of the lines through x disjoint from S′ lie in H. A new infinite family of relative hemisystems on the generalized quadrangle (3,q2) admitting the linear group PSL(2,q) as an automorphism group is constructed. The association schemes arising from our construction are not equivalent to those arising from the Penttila–Williford relative hemisystems.
Relative hemisystems on the Hermitian surface
COSSIDENTE, Antonio
2013-01-01
Abstract
Let S be a generalized quadrangle of order (q 2,q) containing a subquadrangle S′ of order (q,q). Then any line of S either meets S′ in q+1 points or is disjoint from S′. After Penttila and Williford (J. Comb. Theory, Ser. A 118:502–509, 2011), we call a subset H of the lines disjoint from S′ a relative hemisystem of S with respect to S′, provided that for each point x of S∖S′, exactly half of the lines through x disjoint from S′ lie in H. A new infinite family of relative hemisystems on the generalized quadrangle (3,q2) admitting the linear group PSL(2,q) as an automorphism group is constructed. The association schemes arising from our construction are not equivalent to those arising from the Penttila–Williford relative hemisystems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
