Geodesic
Relative hemisystems on the Hermitian surface
Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 275-284.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let S be a generalized quadrangle of order (q $^{2},q$) containing a subquadrangle S$^{\prime}$ of order (q,q). Then any line of S either meets S$^{\prime}$ in q+1 points or is disjoint from S$^{\prime}$. After Penttila and Williford (J. Comb. Theory, Ser. A 118:502-509, 2011), we call a subset H of the lines disjoint from S$^{\prime}$ a relative hemisystem of S with respect to S$^{\prime}$, provided that for each point x of S$\setminus $S$^{\prime}$, exactly half of the lines through x disjoint from S$^{\prime}$ lie in H. A new infinite family of relative hemisystems on the generalized quadrangle $\mathcal{H}(3,q^{2})$ 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.
Keywords: generalized quadrangle, relative hemisystem, association scheme 
@article{JAC_2013__38_2_a9,
     author = {Cossidente, Antonio},
     title = {Relative hemisystems on the {Hermitian} surface},
     journal = {Journal of Algebraic Combinatorics},
     pages = {275--284},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a9/}
}
TY  - JOUR
AU  - Cossidente, Antonio
TI  - Relative hemisystems on the Hermitian surface
JO  - Journal of Algebraic Combinatorics
PY  - 2013
SP  - 275
EP  - 284
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a9/
LA  - en
ID  - JAC_2013__38_2_a9
ER  - 
%0 Journal Article
%A Cossidente, Antonio
%T Relative hemisystems on the Hermitian surface
%J Journal of Algebraic Combinatorics
%D 2013
%P 275-284
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a9/
%G en
%F JAC_2013__38_2_a9
Cossidente, Antonio. Relative hemisystems on the Hermitian surface. Journal of Algebraic Combinatorics, Tome 38 (2013) no. 2, pp. 275-284. http://geodesic.mathdoc.fr/item/JAC_2013__38_2_a9/