Name
Abstract | ||
|---|---|---|
In this paper, by using properties of Baer subplanes, we describe the construction of a minimal blocking set in the Hall plane of order q(2) of size q(2) + 2q + 2 admitting 1-,2-,3-,4-, (q + 1)- and (q + 2)-secants. As a corollary, we obtain the existence of a minimal blocking set of a non-Desarguesian affine plane of order q(2) of size at most 4q(2)/3 + 5q/3, which is considerably smaller than 2q(2) - 1, the Jamison bound for the size of a minimal blocking set in an affine Desarguesian plane of order q(2). We also consider particular Andre planes of order q, where q is a power of the prime p, and give a construction of a small minimal blocking set which admits a secant line not meeting the blocking set in 1 mod p points. Furthermore, we elaborate on the connection of this problem with the study of value sets of certain polynomials and with the construction of small double blocking sets in Desarguesian projective planes; in both topics we provide some new results. |
Year | Venue | Keywords |
|---|---|---|
2016 | ELECTRONIC JOURNAL OF COMBINATORICS | minimal blocking set,Baer subplane,stabiliser of a Baer subplane,Hall plane,Andre plane,double blocking set,value set of polynomials |
Field | DocType | Volume |
Affine transformation,Prime (order theory),Blocking set,Discrete mathematics,Combinatorics,Polynomial,Secant line,Projective plane,Corollary,Mathematics | Journal | 23.0 |
Issue | ISSN | Citations |
2.0 | 1077-8926 | 1 |
PageRank | References | Authors |
0.36 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jan De Beule | 1 | 52 | 11.34 |
| Tamás Héger | 2 | 36 | 5.16 |
| Tamás Szőnyi | 3 | 64 | 11.14 |
| van de voorde | 4 | 35 | 7.85 |