scholarly journals Graph decompositions in projective geometries

2020 ◽  
Vol 29 (3) ◽  
pp. 141-174
Author(s):  
Marco Buratti ◽  
Anamari Nakić ◽  
Alfred Wassermann
Keyword(s):  
Graph Decompositions ◽  
Projective Geometries

Invariants and calculus for projective geometries

1996 ◽  
Vol 306 (1) ◽  
pp. 513-538 ◽  
Author(s):  
A. Rod Gover
Keyword(s):  
Projective Geometries

scholarly journals Tensor Products are Projective Geometries

1997 ◽  
Vol 189 (2) ◽  
pp. 514-528 ◽  
Author(s):  
C.R Leedham-Green ◽  
E.A O'Brien
Keyword(s):  
Tensor Products ◽  
Projective Geometries

scholarly journals Orthogonal Arrays with Parameters $OA(s^3,s^2+s+1,s,2)$ and 3-Dimensional Projective Geometries

10.37236/556 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Kazuaki Ishii
Keyword(s):  
Orthogonal Array ◽  
Prime Power ◽  
Orthogonal Arrays ◽  
3 Dimensional ◽  
Projective Geometries ◽  
Finite Spaces ◽  
Alpha Type

There are many nonisomorphic orthogonal arrays with parameters $OA(s^3,s^2+s+1,s,2)$ although the existence of the arrays yields many restrictions. We denote this by $OA(3,s)$ for simplicity. V. D. Tonchev showed that for even the case of $s=3$, there are at least 68 nonisomorphic orthogonal arrays. The arrays that are constructed by the $n-$dimensional finite spaces have parameters $OA(s^n, (s^n-1)/(s-1),s,2)$. They are called Rao-Hamming type. In this paper we characterize the $OA(3,s)$ of 3-dimensional Rao-Hamming type. We prove several results for a special type of $OA(3,s)$ that satisfies the following condition: For any three rows in the orthogonal array, there exists at least one column, in which the entries of the three rows equal to each other. We call this property $\alpha$-type. We prove the following. (1) An $OA(3,s)$ of $\alpha$-type exists if and only if $s$ is a prime power. (2) $OA(3,s)$s of $\alpha$-type are isomorphic to each other as orthogonal arrays. (3) An $OA(3,s)$ of $\alpha$-type yields $PG(3,s)$. (4) The 3-dimensional Rao-Hamming is an $OA(3,s)$ of $\alpha$-type. (5) A linear $OA(3,s)$ is of $\alpha $-type.

Dualities for infinite-dimensional projective geometries

1995 ◽  
Vol 56 (3) ◽  
pp. 225-236 ◽  
Author(s):  
Claude-Alain Faure ◽  
Alfred Fr�licher
Keyword(s):  
Infinite Dimensional ◽  
Projective Geometries

Projective Geometries and Projective Lattices

2000 ◽  
pp. 25-53
Author(s):  
Claude-Alain Faure ◽  
Alfred Frölicher
Keyword(s):  
Projective Geometries ◽  
Projective Lattices

Projective Geometries that are Disjoint Unions of Caps

1980 ◽  
Vol 32 (6) ◽  
pp. 1299-1305 ◽  
Author(s):  
Barbu C. Kestenband
Keyword(s):  
Finite Field ◽  
Projective Geometry ◽  
Prime Power ◽  
Disjoint Union ◽  
Hermitian Matrices ◽  
Incidence Relation ◽  
Projective Geometries ◽  
Image Position ◽  
Natural Way ◽  
Square Matrix

We show that any PG(2n, q2) is a disjoint union of (q2n+1 − 1)/ (q − 1) caps, each cap consisting of (q2n+1 + 1)/(q + 1) points. Furthermore, these caps constitute the “large points” of a PG(2n, q), with the incidence relation defined in a natural way.A square matrix H = (hij) over the finite field GF(q2), q a prime power, is said to be Hermitian if hijq = hij for all i, j [1, p. 1161]. In particular, hii ∈ GF(q). If if is Hermitian, so is p(H), where p(x) is any polynomial with coefficients in GF(q).Given a Desarguesian Projective Geometry PG(2n, q2), n > 0, we denote its points by column vectors:All Hermitian matrices in this paper will be 2n + 1 by 2n + 1, n > 0.

A parallel fast boundary element method using cyclic graph decompositions

2015 ◽  
Vol 70 (4) ◽  
pp. 807-824 ◽  
Author(s):  
Dalibor Lukáš ◽  
Petr Kovář ◽  
Tereza Kovářová ◽  
Michal Merta
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Graph Decompositions ◽  
Cyclic Graph ◽  
Element Method
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