Jesse Lansdown

activity

20162026

collaborators

16 papers

math.CO2026

On the spherical design properties of a $P$ - and $Q$ -polynomial association scheme

Jesse Lansdown, William J. Martin, Akihiro Munemasa +2

We show that the strength as a spherical design of the spherical embedding of a $P$ - and $Q$ -polynomial association scheme with at least three classes with respect to a $Q$ -polynom…

math.CO2025

Roux schemes which carry association schemes locally

Alexander L. Gavrilyuk, Jesse Lansdown, Akihiro Munemasa +1

A roux scheme is an association scheme formed from a special "roux" matrix and the regular permutation representation of an associated group. They were introduced by Iverson and Mi…

math.CO2024

The synchronisation hierarchy via coherent configurations

John Bamberg, Jesse Lansdown

We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating…

math.CO2024

Rational Delsarte designs and Galois fusions of association schemes

Jesse Lansdown, William J. Martin

Delsarte theory, more specifically the study of codes and designs in association schemes, has proved invaluable in studying an increasing assortment of association schemes in recen…

math.CO2024

Maximum Erdős-Ko-Rado sets of chambers and their antidesigns in vector-spaces of even dimension

Philipp Heering, Jesse Lansdown, Klaus Metsch

A chamber of the vector space $F_{q}^{n}$ is a set ${S_{1}, \dots, S_{n - 1}}$ of subspaces of $F_{q}^{n}$ where $S_{1} \subset S_{2} \subset \dots \subset S_{n - 1}$ and $\dim(S_i)…

math.GR2024

Tactical decompositions in finite polar spaces and non-spreading classical group actions

John Bamberg, Michael Giudici, Jesse Lansdown +1

For finite classical groups acting naturally on the set of points of their ambient polar spaces, the symmetry properties of \emph{synchronising} and \emph{separating} are equivalen…

math.CO2023

On Bruen chains

John Bamberg, Jesse Lansdown, Geertrui Van de Voorde

It is known that a Bruen chain of the three-dimensional projective space $PG (3, q)$ exists for every odd prime power $q$ at most $37$ , except for $q = 29$ . It was shown by Ca…

math.CO2022

Separating rank 3 graphs

John Bamberg, Michael Giudici, Jesse Lansdown +1

We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separati…

math.CO2022

A census of small Schurian association schemes

Jesse Lansdown

Using the classification of transitive groups of degree $n$ , for $2 ⩽ n ⩽ 48$ , we classify the Schurian association schemes of order $n$ , and as a consequence, the…

math.CO2021

Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry

John Bamberg, Jesse Lansdown

In this paper we show that if $θ$ is a $T$ -design of an association scheme $(Ω, R)$ , and the Krein parameters $q_{i, j}^{h}$ vanish for some $h \neq \in T$ and all $i, j \no…

math.GR2021

Synchronising primitive groups of diagonal type exist

John Bamberg, Michael Giudici, Jesse Lansdown +1

Every synchronising permutation group is primitive and of one of three types: affine, almost simple, or diagonal. We exhibit the first known example of a synchronising diagonal typ…

math.CO2021

The Non-Existence of Block-Transitive Subspace Designs

Daniel R. Hawtin, Jesse Lansdown

Let $q$ be a prime power and $V ≅ F_{q}^{n}$ . A $t$ - $(n, k, λ)_{q}$ design, or simply a subspace design, is a pair $D = (V, B)$ , where $B$ is a su…

math.CO2019

A family of hemisystems on the parabolic quadrics

Jesse Lansdown, Alice C. Niemeyer

We constuct a family of hemisystems of the parabolic quadric $Q (2 d, q)$ , for all ranks $d \geq 2$ and all odd prime powers $q$ , that admit $Ω_{3} (q) ≅ PSL_{2} (q)$ …

math.CO2017

The binary $q$ -analogue of the Fano plane has a trivial automorphism group

John Bamberg, Ferdinand Ihringer, Jesse Lansdown +1

A $q$ -analogue of a $t$ -design is a set $S$ of subspaces (of dimension $k$ ) of a finite vector space $V$ over a field of order $q$ such that each $t$ subspace is contained in a con…

math.CO2016

On $m$ -ovoids of regular near polygons

John Bamberg, Jesse Lansdown, Melissa Lee

We generalise the work of Segre (1965), Cameron - Goethals - Seidel (1978), and Vanhove (2011) by showing that nontrivial $m$ -ovoids of the dual polar spaces $D Q (2 d, q)$ , $DW(2d-1,…

math.CO2016

Bruck nets and partial Sherk planes

John Bamberg, Joanna B. Fawcett, Jesse Lansdown

In Bachmann's Aufbau der Geometrie aus dem Spiegelungsbegriff (1959), it was shown that a finite metric plane is a Desarguesian affine plane of odd order equipped with a perpendicu…

On the spherical design properties of a P- and Q-polynomial association scheme

Roux schemes which carry association schemes locally

The synchronisation hierarchy via coherent configurations

Rational Delsarte designs and Galois fusions of association schemes

Maximum Erdős-Ko-Rado sets of chambers and their antidesigns in vector-spaces of even dimension

Tactical decompositions in finite polar spaces and non-spreading classical group actions

On Bruen chains

Separating rank 3 graphs

A census of small Schurian association schemes

Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry

Synchronising primitive groups of diagonal type exist

The Non-Existence of Block-Transitive Subspace Designs

A family of hemisystems on the parabolic quadrics

The binary q-analogue of the Fano plane has a trivial automorphism group

On m-ovoids of regular near polygons

Bruck nets and partial Sherk planes

On the spherical design properties of a $P$ - and $Q$ -polynomial association scheme

The binary $q$ -analogue of the Fano plane has a trivial automorphism group

On $m$ -ovoids of regular near polygons