A stability theorem for lines in Galois planes of prime order

被引：4

作者：

Szonyi, Tamas ^{[1
,2
]}

Weiner, Zsuzsa ^{[1
,3
]}

机构：

[1] Eotvos Lorand Univ, Dept Comp Sci, H-1117 Budapest, Hungary

[2] Hungarian Acad Sci, Comp & Automat Res Inst, H-1111 Budapest, Hungary

[3] Prezi Com, H-1075 Budapest, Hungary

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2012年 / 62卷 / 01期

关键词：

Finite geometry; Galois planes; Blocking sets; Stability theorem; BLOCKING SETS;

D O I：

10.1007/s10623-011-9495-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we prove that a point set of size less than 3/2 (q + 1) in in PG(2, q), q prime, that has relatively few 0-secants must contain many collinear points. More precise bounds can be found in Theorem 4.

引用

页码：103 / 108

页数：6

共 10 条

[1]

[Anonymous], 1973, INFINITE FINITE SETS

[2] BLOCKING SETS IN DESARGUESIAN PROJECTIVE-PLANES [J].

BLOKHUIS, A ;

BROUWER, AE .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1986, 18 :132-134

[3] Covering all points except one [J].

Blokhuis, A. ;

Brouwer, A. E. ;

Szonyi, T. .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2010, 32 (01) :59-66

[4] ON THE SIZE OF A BLOCKING SET IN PG(2,P) [J].

BLOKHUIS, A .

COMBINATORICA, 1994, 14 (01) :111-114

[5] BLOCKING NUMBER OF AN AFFINE SPACE [J].

BROUWER, AE ;

SCHRIJVER, A .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1978, 24 (02) :251-253

[6] BLOCKING SETS IN FINITE PROJECTIVE PLANES [J].

BRUEN, A .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1971, 21 (03) :380-&

[7] BAER SUBPLANES AND BLOCKING SETS [J].

BRUEN, A .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 76 (02) :342-&

[8]

Gacs T., 2003, J GEOM, V76, P256

[9] COVERING FINITE-FIELDS WITH COSETS OF SUBSPACES [J].

JAMISON, RE .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1977, 22 (03) :253-266

[10] Around Redei's theorem [J].

Szönyi, T .

DISCRETE MATHEMATICS, 1999, 208 :557-575

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