3 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 -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 is a -matrix of order with zeros and ones in each row and in each column. Two such squares are orthogonal…
math.CO2025
Weak colourings of Kirkman triple systems
Andrea C. Burgess, Nicholas J. Cavenagh, Peter Danziger +1
A -colouring of the point set of a block design is said to be {\em weak} if no block is monochromatic. The {\em chromatic number} of a block design is the smallest…