Peter Dukes

activity

20232026

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Showing 2024Show all

3 papers · 1 filter

math.CO2024

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.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

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…