2005
DOI: 10.1016/j.disc.2004.12.015
|View full text |Cite
|
Sign up to set email alerts
|

On defining sets for projective planes

Abstract: In this note we prove that projective planes of order q have defining sets of size o(q 2 ), improving a result of Gray et al. [On the size of the smallest defining set of PG(2, q), Bull. Inst. Combin. Appl. 21 (1997) 91-94].

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
39
0
1

Year Published

2007
2007
2020
2020

Publication Types

Select...
5

Relationship

0
5

Authors

Journals

citations
Cited by 23 publications
(40 citation statements)
references
References 12 publications
0
39
0
1
Order By: Relevance
“…Let 1 (2, q) be the smallest size of a 1-saturating set in PG (2, q). In [21,52], for q large enough, by probabilistic methods the following upper bound is proved (for 3 √ 2 see [21, p.24]):…”
Section: Introduction the Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Let 1 (2, q) be the smallest size of a 1-saturating set in PG (2, q). In [21,52], for q large enough, by probabilistic methods the following upper bound is proved (for 3 √ 2 see [21, p.24]):…”
Section: Introduction the Main Resultsmentioning
confidence: 99%
“…The authors of [50] conjecture that the constant C can be reduced to C = 10. A survey and analysis of random constructions for geometrical objects can be found in [21,34,52].…”
Section: Introduction the Main Resultsmentioning
confidence: 99%
“…For the proof the reader is referred to [17]. Note that this is slightly more complicated than just using Lemma 2.3.…”
Section: More Applications Of the Probabilistic Methodsmentioning
confidence: 97%
“…Further results on n(k) can be found in another paper by Kahn [59]. A very slight modification of Kahn's argument can be applied to defining sets of projective planes, as observed in [17]. Gray [42] defined defining sets of designs as follows: A set of blocks which is a subset of a unique t − (v, k, λ) design D is called a defining set of that design.…”
Section: More Delicate Applications Of the Probabilistic Methodsmentioning
confidence: 97%
See 1 more Smart Citation