Journal ArticleDOI
Non-existence of sets of type $$\mathbf (0, 1, 2 , {\varvec{n}}_{{\varvec{d}}})_{{\varvec{d}}}$$ in PG($${\varvec{r,q}}$$r,q) with $$\mathbf 3 \le {\varvec{d}}\le {\varvec{r}}-\mathbf 1 $$3≤d≤r-1 and $${\varvec{r}}\ge \mathbf 4 $$r≥4
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TLDR
In this article, the existence of sets of type (0, 1, 2,n,d,n) = 0, 1 2, 2, n,d = 0.Abstract:
This paper deals with sets of type $$(0,1,2,n_{d})_{d}$$
in PG(r, q), $$1\le d\le r-1$$
. The non-existence of sets of type $$(0,1,2,n_{d})_{d}$$
, $$3\le d\le r-1$$
in PG(r, q) with $$r\ge 4$$
is proved.read more
Citations
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Journal ArticleDOI
A note on sets of type $$(0,mq,2mq)_2$$ ( 0 , m q , 2 m q ) 2 in PG(3, q)
Journal ArticleDOI
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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BookDOI
General Galois geometries
TL;DR: In this paper, the authors define Hermitian varieties, Grassmann varieties, Veronese and Segre varieties, and embedded geometries for finite projective spaces of three dimensions.
Journal ArticleDOI
On Sets with Few Intersection Numbers in Finite Projective and Affine Spaces
TL;DR: All sets of points of both affine and projective spaces over the Galois field $\mathop{\rm{GF}}(q)$ such that every line of the geometry that is neither contained in £X nor disjoint from £X meets the set $X$ in a constant number of points are determined.
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On regular {v, n}‐arcs in finite projective spaces
TL;DR: In this paper, the authors show that if P is a projective plane of order q and S is a regular {v, n}-arc with n ≥ √q + 1 spanning a subspace U of dimension at least 3, then S is an affine space of order Q in U, or S equals the point set of U.
Journal ArticleDOI
A characterization of the sets of internal and external points of a conic
F. De Clerck,N. De Feyter +1 more
TL;DR: This work provides a characterization of the sets of internal and external points of a nondegenerate conic in the plane PG(2,q), q odd, by means of their pattern of intersection with lines.