Wen-Ai Jackson

activity

20122026

most citedExterior splashes and linear sets of rank 3

6 citations · 22 across the 21 of their papers we have counts for

collaborators

21 papers

math.CO2026

The intersection of two linear sets of rank 3 in PG(1,q^3)

S. G. Barwick, Alice M. W. Hui, Wen-Ai Jackson

This article studies the intersection of two linear sets of rank 3 of PG(1,q^3). In particular, all possible intersection sizes are determined, the structure of the largest interse…

math.CO2025

The partition of $P G (2, q^{3})$ arising from an order 3 planar collineation

S. G. Barwick, Alice M. W. Hui, Wen-Ai Jackson

Let $ϕ$ be a collineation of order 3 acting on $P G (2, q^{3})$ whose fixed points are exactly an $F_{q}$ -plane $π_{q}$ . Let $T$ be a point whose orbit under $ϕ$ is a triangle and l…

math.CO2025

The planar projectivity of PG(2, $q^{3}$ ) of order 3 under field reduction

S. G. Barwick, Alice M. W. Hui, Wen-Ai Jackson

Let $ϕ$ be a collineation of $PG (2, q^{3})$ of order 3 which fixes a plane of order $q$ pointwise. The points of $PG (2, q^{3})$ can be parti…

math.CO2022

The feet of orthogonal Buekenhout-Metz unitals

S. G. Barwick, W. -A. Jackson, P. Wild

In this article we look at the geometric structure of the feet of an orthogonal Buekenhout-Metz unital U in PG(2,q^2). We show that the feet of each point form a set of type (0,1,2…

math.CO2019

A characterisation of F_q-conics of PG(2,q^3)

S. G. Barwick, Wen-Ai Jackson, Peter Wild

This article considers an F_q-conic contained in an F_q-subplane of PG(2,q^3), and shows that it corresponds to a normal rational curve in the Bruck-Bose representation in PG(6,q).…

math.CO2019

The Bose representation of PG(2,q^3) in PG(8,q)

S. G. Barwick, Wen-Ai Jackson, Peter Wild

This article looks at the Bose representation of $P G (2, q^{3})$ as a 2-spread of $P G (8, q)$ . It is shown that an $F_{q}$ -subline of $P G (2, q^{3})$ corresponds to a 2-regulus, and an…

math.CO2019

Characterising hyperbolic hyperplanes of a non-singular quadric in $P G (4, q)$

S. G. Barwick, Alice M. W. Hui, Wen-Ai Jackson +1

Let $H$ be a non-empty set of hyperplanes in $P G (4, q)$ , $q$ even, such that every point of $P G (4, q)$ lies in either $0$ , $\frac{1}{2} q^{3}$ or $\frac{1}{2} (q^{3} + q^{2})$ hyperplanes of $H$ , and…

math.CO2019

A characterisation of Baer subplanes

S. G. Barwick, Wen-Ai Jackson

Let $K$ be a set of $q^{2} + 2 q + 1$ points in $P G (4, q)$ . We show that if every 3-space meets $K$ in either one, two or three lines, a line and a non-degenerate conic, or a twisted cubic…

math.CO2019

Characterising elliptic solids of $Q (4, q)$ , $q$ even

S. G. Barwick, Alice M. W. Hui, Wen-Ai Jackson

Let $E$ be a set of solids (hyperplanes) in $P G (4, q)$ , $q$ even, $q > 2$ , such that every point of $P G (4, q)$ lies in either $0$ , $\frac{1}{2} q^{3}$ or $\frac{1}{2} (q^{3} - q^{2})$ solids of $E$ , and…

math.CO2019

Conics in Baer subplanes

S. G. Barwick, Wen-Ai Jackson, Peter Wild

This article studies conics and subconics of $P G (2, q^{2})$ and their representation in the André/Bruck-Bose setting in $P G (4, q)$ . In particular, we investigate their relationship wit…

math.CO2019★ 1 cited

Specialness and the Bose representation

S. G. Barwick, Wen-Ai Jackson, Peter Wild

This article looks at subconics of order $q$ of $P G (2, q^{2})$ and characterizes them in the Bruck-Bose representation in $P G (4, q)$ . In common with other objects in the Bruck-Bose rep…

math.CO2016★ 3 cited

New families of strongly regular graphs

S. G. Barwick, Wen-Ai Jackson, Tim Penttila

In this article we construct a series of new infinite families of strongly regular graphs with the same parameters as the point-graphs of non-singular quadrics in PG(n,2).

math.CO2014★ 1 cited

The exterior splash in $P G (6, q)$ : Special conics

S. G. Barwick, Wen-Ai Jackson

Let $π$ be an order- $q$ -subplane of $P G (2, q^{3})$ that is exterior to $ℓ_{\infty}$ . The exterior splash of $π$ is the set of $q^{2} + q + 1$ points on $ℓ_{\infty}$ that lie on an extende…

math.CO2014

Hyper-reguli in PG(5,q)

S. G. Barwick, Wen-Ai Jackson

A simple counting argument is used to show that for all $q$ , an André hyper-regulus $X$ in $P G (5, q)$ has exactly two switching sets. Moreover, there are exactly $2(q^2+q+1)…

math.CO2014

The exterior splash in PG(6,q): Transversals

S. G. Barwick, Wen-Ai Jackson

Let $π$ be an order- $q$ -subplane of $P G (2, q^{3})$ that is exterior to $ℓ_{\infty}$ . Then the exterior splash of $π$ is the set of $q^{2} + q + 1$ points on $ℓ_{\infty}$ that lie on an ex…

math.CO2014★ 6 cited

Exterior splashes and linear sets of rank 3

S. G. Barwick, Wen-Ai Jackson

In $\PG(2,q^3)$, let $π$ be a subplane of order $q$ that is exterior to $\li$. The exterior splash of $π$ is defined to be the set of $q^{2} + q + 1$ points on $\li$ that lie on a line o…

math.CO2013★ 3 cited

Characterising pointsets in PG(4,q) that correspond to conics

S. G. Barwick, Wen-Ai Jackson

We consider a non-degenerate conic in $\PG(2,q^2)$, $q$ odd, that is tangent to $ℓ_{\infty}$ and look at its structure in the Bruck-Bose representation in $\PG(4,q)$. We determine…

math.CO2013★ 4 cited

The tangent splash in $\PG(6,q)$

S. G. Barwick, Wen-Ai Jackson

Let B be a subplane of PG(2,q^3) of order q that is tangent to $ℓ_{\infty}$ . Then the tangent splash of B is defined to be the set of q^2+1 points of $ℓ_{\infty}$ that lie on a l…

math.CO2013★ 1 cited

A characterisation of translation ovals in finite even order planes

S. G. Barwick, Wen-Ai Jackson

In this article we consider a set C of points in PG(4,q), q even, satisfying certain combinatorial properties with respect to the planes of PG(4,q). We show that there is a regular…

math.CO2013★ 3 cited

An investigation of the tangent splash of a subplane of PG(2,q^3)

S. G. Barwick, Wen-Ai Jackson

In $P G (2, q^{3})$ , let $π$ be a subplane of order $q$ that is tangent to $ℓ_{i} n f t y$ . The tangent splash of $π$ is defined to be the set of $q^{2} + 1$ points on $ℓ_{i} n f t y$ that lie on…

math.CO2012

A Characterisation of Tangent Subplanes of PG(2,q^3)

S. G. Barwick, Wen-Ai Jackson

In: S.G. Barwick and W.A. Jackson. Sublines and subplanes of PG(2,q^3) in the Bruck--Bose representation in PG(6,q). Finite Fields Th. App. 18 (2012) 93--107., the authors determin…

The intersection of two linear sets of rank 3 in PG(1,q^3)

The partition of PG(2,q3) arising from an order 3 planar collineation

The planar projectivity of PG(2, q3) of order 3 under field reduction

The feet of orthogonal Buekenhout-Metz unitals

A characterisation of F_q-conics of PG(2,q^3)

The Bose representation of PG(2,q^3) in PG(8,q)

Characterising hyperbolic hyperplanes of a non-singular quadric in PG(4,q)

A characterisation of Baer subplanes

Characterising elliptic solids of Q(4,q), q even

Conics in Baer subplanes

Specialness and the Bose representation

New families of strongly regular graphs

The exterior splash in PG(6,q): Special conics

Hyper-reguli in PG(5,q)

The exterior splash in PG(6,q): Transversals

Exterior splashes and linear sets of rank 3

Characterising pointsets in PG(4,q) that correspond to conics

The tangent splash in $\PG(6,q)$

A characterisation of translation ovals in finite even order planes

An investigation of the tangent splash of a subplane of PG(2,q^3)

A Characterisation of Tangent Subplanes of PG(2,q^3)

The partition of $P G (2, q^{3})$ arising from an order 3 planar collineation

The planar projectivity of PG(2, $q^{3}$ ) of order 3 under field reduction

Characterising hyperbolic hyperplanes of a non-singular quadric in $P G (4, q)$

Characterising elliptic solids of $Q (4, q)$ , $q$ even

The exterior splash in $P G (6, q)$ : Special conics