论文信息 - Blocking Sets of Size qt+qt-1+1

Blocking Sets of Size qt+qt-1+1

We prove that in the desarguesian plane PG(2, qt) (t>4) there are at least three inequivalent blocking sets of size qt+qt?1+1. The first one has q+1 Redei lines, the second one has exactly one Redei line, and the third one is not of Redei type. For GF(q) the largest subfield of GF(qt), our results disprove a conjecture quoted by A. Blokhuis (1998, in “Galois Geometry and Generalized Polygons,” Gent).

Olga Polverino | Guglielmo Lunardon | G. Lunardon | O. Polverino

[1] P. Dembowski. Finite geometries , 1997 .

[2] Olga Polverino,et al. On Small Blocking Sets , 1998, Comb..

[3] Bogdan Oporowski,et al. Partitioning Graphs of Bounded Tree-Width , 1998, Comb..

[4] Monique Limbos. A characterisation of the embeddings of PG(m,q) into PG(n,qr). , 1981 .

[5] Tamás Szőnyi,et al. Lacunary Polynomials, Multiple Blocking Sets and Baer Subplanes , 1999 .

[6] Guglielmo Lunardon,et al. Linear k-blocking Sets , 2001, Comb..

[7] Minimal blocking sets in finite planes , 1992 .

[8] T. Szonyi. Blocking Sets in Desarguesian Affine and Projective Planes , 1997 .

[9] A. Bruen,et al. Baer subplanes and blocking sets , 1970 .