Peter Dukes

activity

20242026

collaborators

Showing math.COShow all

6 papers · 1 filter

math.CO2026

Fuzzy latin squares and balanced permutation pattern statistics

Joy Cooper, Peter J. Dukes

A latin square of order $n$ can be viewed as a partition of the $n \times n$ all-ones matrix into permutation matrix summands. Here, we consider a relaxation in which the matrix su…

math.CO2026

On decomposition thresholds for odd-length cycles and other tripartite graphs

Darryn Bryant, Peter Dukes, Daniel Horsley +2

An (edge) decomposition of a graph $G$ is a set of subgraphs of $G$ whose edge sets partition the edge set of $G$ . Here we show, for each odd $ℓ \geq 5$ , that any graph $G$ of s…

math.CO2026

Intersection numbers of Sudoku latin squares

Jade S. Davies, Peter J. Dukes

Let $n = h w$ , where $h$ and $w$ are integers with $h, w \geq 2$ . We determine the set of possible intersection numbers of two $n \times n$ latin squares having the additional `Sudoku'…

math.CO2025

Duplicated Steiner triple systems with self-orthogonal near resolutions

Peter J. Dukes, Esther R. Lamken

A Steiner triple system, STS $(v)$ , is a family of $3$ -subsets (blocks) of a set of $v$ elements such that any two elements occur together in precisely one block. A collection of tr…

math.CO2024

The balancing index over the alternating group

Peter Dukes, Georgia Penner

The balancing index of a polynomial $f \in Z [x_{1}, \dots, x_{n}]$ is the least positive sum of coefficients in an integer linear combination of permuted copies of $f$ which pro…

math.CO2024

The linear system for Sudoku and a fractional completion threshold

Peter J. Dukes, Kate Nimegeers

We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, w…