Nicholas J. Cavenagh

activity

20072026

most citedLatin trades in groups defined on planar triangulations

10 citations · 31 across the 22 of their papers we have counts for

collaborators

25 papers

math.CO2026

Defining sets which intersect each Latin trade at least twice

Richard Bean, Nicholas Cavenagh

A defining set of a Latin square is a partially filled-in Latin square which completes to no other Latin square of the same order. We introduce the concept of a $k$ -strong defining…

math.CO2025

Maximal sets of mutually orthogonal frequency squares and Doehlert-Klee designs

Carly Bodkin, Nicholas J. Cavenagh, Ian M. Wanless

A binary frequency square of type $(n; λ_{0}, λ_{1})$ is a $(0, 1)$ -matrix of order $n$ with $λ_{0}$ zeros and $λ_{1}$ ones in each row and in each column. Two such squares are orthogonal if…

math.CO2024

Weak colourings of Kirkman triple systems

Andrea C. Burgess, Nicholas J. Cavenagh, Peter Danziger +1

A $δ$ -colouring of the point set of a block design is said to be {\em weak} if no block is monochromatic. The {\em chromatic number} $χ (S)$ of a block design $S$ is the smallest in…

math.CO2023

Latin bitrades derived from quasigroup autoparatopisms

Nicholas Cavenagh, Raúl Falcón

In 2008, Cavenagh and Drápal, et al, described a method of constructing Latin trades using groups. The Latin trades that arise from this construction are entry-transitive (that is,…

math.CO2022

Mutually orthogonal frequency rectangles

Fahim Rahim, Nicholas J. Cavenagh

A frequency rectangle of type FR $(m, n; q)$ is an $m \times n$ matrix such that each symbol from a set of size $q$ appears $n / q$ times in each row and $m / q$ times in each column. Two…