J. Allsop

activity

20212026

most citedRow-Hamiltonian Latin squares and Falconer varieties

5 citations · 10 across the 10 of their papers we have counts for

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12 papers · 1 filter

math.CO2026

Improved bounds on completion of partial Latin squares

Jack Allsop, Candida Bowtell, Thomas Lesgourgues +1

A Latin square of order $n$ is an $n \times n$ array filled with $n$ symbols so that each symbol appears exactly once in every row and column. A partial Latin square of order $n$ i…

math.CO2026

Universal probability bounds for partial Latin squares

Jack Allsop, Patrick Morris

This paper studies the probability of substructures occurring in random Latin squares. Our main result states that if $α, β > 0$ are such that $2 α + β < 1$ , then there are positive consta…

math.CO2025

Spanning Components and Surfaces Under Minimum Vertex Degree

Jack Allsop, Ander Lamaison, Richard Lang +1

We study minimum vertex-degree conditions in 3-uniform hypergraphs for (tight) spanning components and (combinatorial) surfaces. Our main results show that a 3-uniform hypergraph $…

math.CO2025

Outline Rectangles, Allocations, and Latin Young Diagrams

Jack Allsop, Daniel Kotlar, Ian Wanless

A Young diagram is \emph{Latin} if there is an assignment of integers to its cells so that each row $i$ of length $l_{i}$ is populated by the numbers $1, \dots, l_{i}$ , and the numbers…

math.CO2025

Isotopisms of quadratic quasigroups

Jack Allsop

A quasigroup is a pair $(Q, \cdot)$ where $Q$ is a non-empty set and $\cdot$ is a binary operation on $Q$ such that for every $(u, v) \in Q^{2}$ there exists a unique $(x, y) \in Q^2…

math.CO2025

Perfect $1$ -factorisations of $K_{11, 11}$

Jack Allsop, Ian M. Wanless

A perfect $1$ -factorisation of a graph is a decomposition of that graph into $1$ -factors such that the union of any two $1$ -factors is a Hamiltonian cycle. A Latin square of order…

math.CO2024

Commuting Pairs in Quasigroups

Jack Allsop, Ian M. Wanless

A quasigroup is a pair $(Q, *)$ where $Q$ is a non-empty set and $*$ is a binary operation on $Q$ such that for every $(a, b) \in Q^{2}$ there exists a unique $(x, y) \in Q^{2}$ such t…

math.CO2024

Subsquares in random Latin rectangles

Jack Allsop, Ian M. Wanless

Suppose that $k$ is a function of $n$ and $n \to \infty$ . We show that with probability $1 - O (1/ n)$ , a uniformly random $k \times n$ Latin rectangle contains no proper Latin subsquare…

math.CO2023★ 2 cited

Latin squares without proper subsquares

Jack Allsop, Ian M. Wanless

A $d$ -dimensional Latin hypercube of order $n$ is a $d$ -dimensional array containing symbols from a set of cardinality $n$ with the property that every axis-parallel line contains…

math.CO2023★ 3 cited

Cycles of quadratic Latin squares and anti-perfect $1$ -factorisations

Jack Allsop

A Latin square of order $n$ is an $n \times n$ matrix of $n$ symbols, such that each symbol occurs exactly once in each row and column. For an odd prime power $q$ let $\mathbb{F}_q…

math.CO2022★ 5 cited

Row-Hamiltonian Latin squares and Falconer varieties

Jack Allsop, Ian M. Wanless

A \emph{Latin square} is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square $L$ is \emph{row-Hamiltonian} if the permutation induc…

math.CO2021

Degree of Orthomorphism Polynomials over Finite Fields

Jack Allsop, Ian M. Wanless

An orthomorphism over a finite field $F_{q}$ is a permutation $θ : F_{q} \mapsto F_{q}$ such that the map $x \mapsto θ (x) - x$ is also a permutation of $F_{q}$ .…

Improved bounds on completion of partial Latin squares

Universal probability bounds for partial Latin squares

Spanning Components and Surfaces Under Minimum Vertex Degree

Outline Rectangles, Allocations, and Latin Young Diagrams

Isotopisms of quadratic quasigroups

Perfect 1-factorisations of K11,11​

Commuting Pairs in Quasigroups

Subsquares in random Latin rectangles

Latin squares without proper subsquares

Cycles of quadratic Latin squares and anti-perfect 1-factorisations

Row-Hamiltonian Latin squares and Falconer varieties

Degree of Orthomorphism Polynomials over Finite Fields

Perfect $1$ -factorisations of $K_{11, 11}$

Cycles of quadratic Latin squares and anti-perfect $1$ -factorisations