A characterization of the natural embedding of the split Cayley hexagon H(q) in PG(6,q) by intersection numbers

2008 ◽  
Vol 29 (6) ◽  
pp. 1502-1506 ◽  
Author(s):  
Joseph A. Thas ◽  
Hendrik Van Maldeghem
Keyword(s):  
Intersection Numbers ◽  
Natural Embedding ◽  
Split Cayley Hexagon

scholarly journals The linear programming relaxation permutation symmetry group of an orthogonal array defining integer linear program

2016 ◽  
Vol 19 (1) ◽  
pp. 206-216 ◽  
Author(s):  
David M. Arquette ◽  
Dursun A. Bulutoglu
Keyword(s):  
Linear Programming ◽  
Symmetry Group ◽  
Integer Linear Programming ◽  
Orthogonal Array ◽  
Complete Characterization ◽  
Linear Programming Relaxation ◽  
Permutation Symmetry ◽  
Natural Embedding ◽  
Lp Relaxation

There is always a natural embedding of $S_{s}\wr S_{k}$ into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation with equality constraints. The point of this paper is to prove that in the $2$-level, strength-$1$ case the LP relaxation permutation symmetry group of this formulation is isomorphic to $S_{2}\wr S_{k}$ for all $k$, and in the $2$-level, strength-$2$ case it is isomorphic to $S_{2}^{k}\rtimes S_{k+1}$ for $k\geqslant 4$. The strength-$2$ result reveals previously unknown permutation symmetries that cannot be captured by the natural embedding of $S_{2}\wr S_{k}$. We also conjecture a complete characterization of the LP relaxation permutation symmetry group of the ILP formulation.Supplementary materials are available with this article.

CHARACTERIZING HERMITIAN VARIETIES IN THREE- AND FOUR-DIMENSIONAL PROJECTIVE SPACES

2018 ◽  
Vol 107 (1) ◽  
pp. 1-8 ◽  
Author(s):  
ANGELA AGUGLIA
Keyword(s):  
Projective Spaces ◽  
Intersection Numbers

We characterize Hermitian cones among the surfaces of degree$q+1$of$\text{PG}(3,q^{2})$by their intersection numbers with planes. We then use this result and provide a characterization of nonsingular Hermitian varieties of$\text{PG}(4,q^{2})$among quasi-Hermitian ones.

A characterization of quadrics by intersection numbers

2007 ◽  
Vol 47 (1-3) ◽  
pp. 165-175 ◽  
Author(s):  
Jeroen Schillewaert
Keyword(s):  
Intersection Numbers

scholarly journals A Characterization of the Hermitian Variety in Finite 3-Dimensional Projective Spaces

10.37236/3416 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Vito Napolitano
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Intersection Numbers ◽  
Combinatorial Characterization ◽  
Hermitian Variety ◽  
3 Dimensional ◽  
Dimensional Projective Space

A combinatorial characterization of a non-singular Hermitian variety of the finite 3-dimensional projective space via its intersection numbers with respect to lines and planes is given.   A corrigendum was added on March 29, 2019.

scholarly journals On Baer cones in $$\mathrm {PG}(3, q)$$

2021 ◽  
Vol 112 (3) ◽  
Author(s):  
Vito Napolitano
Keyword(s):  
Projective Space ◽  
Prime Power ◽  
Intersection Numbers ◽  
Link Type ◽  
Similar Characterization

AbstractRecently, in Innamorati and Zuanni (J. Geom 111:45, 2020. 10.1007/s00022-020-00557-0) the authors give a characterization of a Baer cone of $$\mathrm {PG}(3, q^2)$$ PG ( 3 , q 2 ) , q a prime power, as a subset of points of the projective space intersected by any line in at least one point and by every plane in $$q^2+1$$ q 2 + 1 , $$q^2+q+1$$ q 2 + q + 1 or $$q^3+q^2+1$$ q 3 + q 2 + 1 points. In this paper, we show that a similar characterization holds even without assuming that the order of the projective space is a square, and weakening the assumptions on the three intersection numbers with respect to the planes.

Sign in / Sign up

Export Citation Format

Share Document