Journal ArticleDOI
On standard two-intersection sets in PG ( r , q )
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This paper extends and analyzes in a finite projective space of any dimension the notion of standard two-intersection sets previously introduced in the projective plane by Penttila and Royle and gets further standardTwo-Intersection sets by applying elementary set-theoretical operations to the elements of the pair.Abstract:
In this paper, we extend and analyze in a finite projective space of any dimension the notion of standard two-intersection sets previously introduced in the projective plane by Penttila and Royle (Des Codes Cryptogr 6:229–245, 1995), see also Blokhuis and Lavrauw (J Combin Theory Ser A 99:377–382, 2002). Moreover, given a pair of suitable distinct standard two-intersection sets in a finite projective space it is possible to get further standard two-intersection sets by applying elementary set-theoretical operations to the elements of the pair.read more
Citations
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A note on sets of type $$(0,mq,2mq)_2$$ ( 0 , m q , 2 m q ) 2 in PG(3, q)
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A characterization of the set of internal points of a conic in PG(2,q), q odd
Stefano Innamorati,Fulvio Zuanni +1 more
TL;DR: In this article, the outer points of a non-degenerate conic C in PG(2, q), q odd, are classified into two kinds of outer points.
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An excursion in finite geometry
TL;DR: A particular Pappus configuration gives us the road map for an excursion into the world of small finite geometries as mentioned in this paper, which is the basis for our work here.
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The type of a point and a characterization of the set of external points of a conic in PG(2, q), q odd
TL;DR: In this paper, the set of external points of a conic in PG, (2, q) odd, within the odd set of points of the conic is characterized.
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Note on the ascent of incidence class of projective sets
TL;DR: In this paper, the authors established the class of H with respect to the planes and proved that H is a set of classes [1, q + 1, q 2 + 1]1 in PG(r, q 3, r ≥ 3, q a prime power].
References
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Journal ArticleDOI
Sets of type ( m, n ) in the affine and projective planes of order nine
Tim Penttila,Gordon F. Royle +1 more
TL;DR: The results of exhaustive computer searches for sets of points of type (m, n) in the projective and affine planes of order nine are given, leading to the conclusion that sets of types are far more numerous than was previously thought.
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Sets of Type (a, b) From Subgroups of ΓL(1, p R )
TL;DR: In this article, Singer cycles are used to construct sets of type (i>a, i>b) with respect to hyperplanes in finite projective spaces using powers of Singer cycles.
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On two-intersection sets with respect to hyperplanes in projective spaces
Aart Blokhuis,Michel Lavrauw +1 more
TL;DR: It is proved that although they have the same parameters, they are different in the special case where r =3 and t =4.
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The geometry of some two-character sets
TL;DR: In this paper, geometric constructions of two-character projective sets are given, which mainly involve commuting polarities, symplectic polarities and normal line-spreads of projective spaces.
Some strongly regular graphs with the parameters of Paley graphs.
Liz Lane-Harvard,Tim Penttila +1 more
TL;DR: Two-intersection sets in PG(5, q), q odd, admitting PSL(2, q) are constructed, whose associated strongly regular graphs have the same parameters as, but are not isomorphic to, Paley graphs.