W. Martin

activity

20022026

most citedCommutative association schemes

70 citations · 144 across the 16 of their papers we have counts for

collaborators

18 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.CO2026

Skirting the $n$ -tuples

Sam Adriaensen, Ferdinand Ihringer, William J. Martin +1

Let $n \geq 2$ and $q \geq 2$ be given. The set $X = Z_{q}^{n}$ is a metric space of diameter $n$ under the Hamming metric $d (\cdot, \cdot)$ . We seek a smallest set $S \subseteq X$ t…

math.CO2025

The Lie algebra $sl_{4} (C)$ and the hypercubes

William J. Martin, Paul Terwilliger

We describe a relationship between the Lie algebra $sl_{4} (C)$ and the hypercube graphs. Consider the $C$ -algebra $P$ of polynomials in four commuting vari…

math.GR2024

Uniqueness and explicit computation of mates in near-factorizations

Donald L. Kreher, William J. Martin, Douglas R. Stinson

We show that a "mate'' $B$ of a set $A$ in a near-factorization $(A, B)$ of a finite group $G$ is unique. Further, we describe how to compute the mate $B$ very efficiently using an…

math.CO2023

Dispersed graph labellings

William J. Martin, Douglas R. Stinson

A $k$ -dispersed labelling of a graph $G$ on $n$ vertices is a labelling of the vertices of $G$ by the integers $1, \dots, n$ such that $d (i, i + 1) \geq k$ for $1 \leq i \leq n - 1$ . $…

math.CO2022

Quantum isomorphism of graphs from association schemes

Ada Chan, William J. Martin

We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arisin…

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

Skirting the n-tuples