A t-semiarc is a point set S_t with the property that the number of tangent lines to S_t at each of its points is t. We show that if a small t-semiarc S_t in PG(2,q) has a large collinear subset K, then the tangents to S_t at the points of K can be blocked by t points not in K. In fact, we give a more general result for small point sets with less uniform tangent distribution. We show that in PG(2,q) small t-semiarcs are related to certain small blocking sets and give some characterization theorems for small semiarcs with large collinear subsets.
Semiarcs with a long secant in PG(2, q) / Csajbok, Bence; T., Heger; G., Kiss. - In: INNOVATIONS IN INCIDENCE GEOMETRY. - ISSN 1781-6475. - STAMPA. - 14:1(2015), pp. 1-26. [10.2140/iig.2015.14.1]
Semiarcs with a long secant in PG(2, q)
Bence Csajbok;
2015-01-01
Abstract
A t-semiarc is a point set S_t with the property that the number of tangent lines to S_t at each of its points is t. We show that if a small t-semiarc S_t in PG(2,q) has a large collinear subset K, then the tangents to S_t at the points of K can be blocked by t points not in K. In fact, we give a more general result for small point sets with less uniform tangent distribution. We show that in PG(2,q) small t-semiarcs are related to certain small blocking sets and give some characterization theorems for small semiarcs with large collinear subsets.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
