Tara Kemp

collaborators

5 papers

math.CO2026

Latin squares with non-partitioning disjoint subsquares

Tara Kemp

A latin square of order $n$ with pairwise disjoint subsquares of orders $h_{1}, \dots, h_{k}$ such that $h_{1} + \dots + h_{k} = n$ is known as a realization. The existence of realizations is a…

math.CO2026

Colourings of Uniform Group Divisible Designs and Maximum Packings

Andrea C Burgess, Peter Danziger, Diane Donovan +4

A weak $c$ -colouring of a design is an assignment of colours to its points from a set of $c$ available colours, such that there are no monochromatic blocks. A colouring of a design…

math.CO2025

Latin cubes with disjoint subcubes of two orders

Tara Kemp, James G. Lefevre

Given a partition $h_{1} + h_{2} + \dots + h_{k} = n$ , a latin square of order $n$ with pairwise disjoint subsquares of orders $h_{1}, \dots, h_{k}$ is called a realization. When the values $h_{i}$ a…

math.CO2025

Latin squares with three disjoint subsquares of the same order

Tara Kemp, James G. Lefevre

Given an integer partition $P = (h_{1} h_{2} \dots h_{k})$ of $n$ , a realization of $P$ is a latin square with disjoint subsquares of orders $h_{1}, h_{2}, \dots, h_{k}$ . Most known results restric…

math.CO2025

Further results on latin squares with disjoint subsquares using rational outline squares

Tara Kemp, James Lefevre

In this paper we consider the problem of finding latin squares with sets of pairwise disjoint subsquares. We develop a new necessary condition on the sizes of the subsquares which…