On the chromatic index of a finite projective space

1989 ◽  
Vol 32 (3) ◽  
Author(s):  
Albrecht Beutelspacher ◽  
Dieter Jungnickel ◽  
ScottA. Vanstone
Keyword(s):  
Projective Space ◽  
Finite Projective Space ◽  
Chromatic Index

scholarly journals The maximum size of a partial spread in a finite projective space

2017 ◽  
Vol 152 ◽  
pp. 353-362 ◽  
Author(s):  
Esmeralda L. Năstase ◽  
Papa A. Sissokho
Keyword(s):  
Projective Space ◽  
Maximum Size ◽  
Finite Projective Space ◽  
Partial Spread

The polynomial degree of the Grassmannian G(1,n,q) of lines in finite projective space PG(n, q)

2006 ◽  
Vol 40 (3) ◽  
pp. 335-341 ◽  
Author(s):  
David G. Glynn ◽  
Johannes G. Maks ◽  
Rey Casse
Keyword(s):  
Projective Space ◽  
Finite Projective Space ◽  
Polynomial Degree

The transitive t-parallelisms of a finite projective space

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Norman L. Johnson ◽  
Alessandro Montinaro
Keyword(s):  
Projective Space ◽  
Finite Projective Space

A characterization of sets of n points which determine n hyperplanes

1968 ◽  
Vol 64 (3) ◽  
pp. 585-588 ◽  
Author(s):  
J. G. Basterfield ◽  
L. M. Kelly
Keyword(s):  
Projective Space ◽  
The Other ◽  
Finite Projective Space ◽  
Other Hand ◽  
Finite Set ◽  
Set Of Points

Suppose N is a set of points of a d-dimensional incidence space S and {Ha}, a ∈ I, a set of hyperplanes of S such that Hi ∈ {Ha} if and only if Hi ∩ N spans Hi. N is then said to determine {Ha}. We are interested here in the case in which N is a finite set of n points in S and I = {1, 2,…, n}; that is to say when a set of n points determines precisely n hyperplanes. Such a situation occurs in E3, for example, when N spans E3 and is a subset of two (skew) lines, or in E2 if N spans the space and n − 1 of the points are on a line. On the other hand, the n points of a finite projective space determine precisely n hyperplanes so that the structure of a set of n points determining n hyperplanes is not at once transparent.

Some Configurations in Finite Projective Spaces and Partially Balanced Incomplete Block Designs

1965 ◽  
Vol 17 ◽  
pp. 114-123 ◽  
Author(s):  
D. K. Ray-Chaudhuri
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Finite Projective Space ◽  
Block Designs ◽  
Incomplete Block ◽  
Finite Plane ◽  
Balanced Incomplete Block Designs ◽  
Pbib Design ◽  
Finite Projective Spaces ◽  
Balanced Incomplete Block

Using the methods developed in (2 and 3), in this paper we study some properties of the configuration of generators and points of a cone in an w-dimensional finite projective space. The configuration of secants and external points of a quadric in a finite plane of even characteristic is also studied. I t is shown that these configurations lead to several series of partially balanced incomplete block (PBIB) designs. PBIB designs are defined in Bose and Shimamoto (1). A PBIB design with m associate classes is an arrangement of v treatments in b blocks such that.

Generalized quadrangles weakly embedded in finite projective space

1998 ◽  
Vol 73 (1-2) ◽  
pp. 353-361 ◽  
Author(s):  
J.A. Thas ◽  
H.Van Maldeghem
Keyword(s):  
Projective Space ◽  
Finite Projective Space ◽  
Generalized Quadrangles

Twelve points in PG (5, 3) with 95040 self-transformations

1958 ◽  
Vol 247 (1250) ◽  
pp. 279-293 ◽  
Keyword(s):  
Projective Space ◽  
Outer Automorphism ◽  
Special Property ◽  
Steiner System ◽  
Finite Projective Space ◽  
Mathieu Group ◽  
Five Dimensions ◽  
Ordinary Space ◽  
High Degree ◽  
Geometrical Realization

The title of this paper could have been ‘Geometry in five dimensions over GF (3)’ (cf. Edge 1954), or ‘The geometry of the second Mathieu group’, or ‘Duads and synthemes’, or ‘Hexastigms’, or simply ‘Some thoughts on the number 6’. The words actually chosen acknowledge the inspiration of the late H. F. Baker, whose last book (Baker 1946) develops the idea of duads and synthemes in a different direction. The special property of the number 6 that makes the present development possible is the existence of an outer automorphism for the symmetric group of this degree. The consequent group of order 1440 is described abstractly in §1, topologically in §2, and geometrically in §§3 to 7. The kernel of the geometrical discussion is in §5, where the chords of a non-ruled quadric in the finite projective space PG (3, 3) are identified with the edges of a graph having an unusually high degree of regularity (Tutte 1958). It is seen in §4 that the ten points which constitute this quadric can be derived very simply from a ‘hexastigm ’ consisting of six points in PG (4, 3) (cf. Coxeter 1958). The connexion with Edge’s work is described in §6. Then §7 shows that the derivation of the quadric from a hexastigm can be carried out in two distinct ways, sug­gesting the use of a second hexastigm in a different 4-space. It is found in §8 that the consequent configuration of twelve points in PG (5, 3) can be divided into two hexastigms in 66 ways. The whole set of 132 hexastigms forms a geometrical realization of the Steiner system s (5, 6, 12), whose group is known to be the quintuply transitive Mathieu group M 12 , of order 95040. Finally, §9 shows how the same 5-dimensional configuration can be regarded (in 396 ways) as a pair of mutually inscribed simplexes, like Möbius’s mutually inscribed tetrahedra in ordinary space of 3 dimensions.

scholarly journals Hermitian Varieties in a Finite Projective Space PG(N, q2)

1966 ◽  
Vol 18 ◽  
pp. 1161-1182 ◽  
Author(s):  
R. C. Bose ◽  
I. M. Chakravarti
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Galois Field ◽  
Finite Projective Space ◽  
Finite Projective Spaces

The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another class of varieties, which we call Hermitian varieties and which have many properties analogous to quadrics. Hermitian varieties are defined only for finite projective spaces for which the ground (Galois field) GF(q2) has order q2, where q is the power of a prime. If h is any element of GF(q2), then = hq is defined to be conjugate to h.

scholarly journals The Geometry of Elation Groups of a Finite Projective Space

2012 ◽  
Vol 10 (1) ◽  
pp. 439-448
Author(s):  
Nicola Durante ◽  
Alessandro Siciliano
Keyword(s):  
Projective Space ◽  
Finite Projective Space
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