Association schemes from the action of $PGL(2,q)$ fixing a nonsingular conic in PG(2,q)
| dc.creator | Hollmann, Henk D. L. | |
| dc.creator | Xiang, Qing | |
| dc.date | 2005-03-24 | |
| dc.date.accessioned | 2026-07-07T05:18:26Z | |
| dc.date.available | 2026-07-07T05:18:26Z | |
| dc.description | The group $PGL(2,q)$ has an embedding into $PGL(3,q)$ such that it acts as the group fixing a nonsingular conic in $PG(2,q)$. This action affords a coherent configuration $R(q)$ on the set $L(q)$ of non-tangent lines of the conic. We show that the relations can be described by using the cross-ratio. Our results imply that the restrictions $R_{+}(q)$ and $R_{-}(q)$ to the sets $L_{+}(q)$ of secant lines and to the set $L_{-}(q)$ of exterior lines, respectively, are both association schemes; moreover, we show that the elliptic scheme $R_{-}(q)$ is pseudocyclic. We further show that the coherent configuration $R(q^2)$ with $q$ even allow certain fusions. These provide a 4-class fusion of the hyperbolic scheme $R_{+}(q^2)$, and 3-class fusions and 2-class fusions (strongly regular graphs) of both schemes $R_{+}(q^2)$ and $R_{-}(q^2). The fusion results for the hyperbolic case are known, but our approach here as well as our results in the elliptic case are new. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503573 | |
| dc.identifier | http://arxiv.org/abs/math/0503573 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74659 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E30 | |
| dc.title | Association schemes from the action of $PGL(2,q)$ fixing a nonsingular conic in PG(2,q) | |
| dc.type | text |