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

Showing 2016Show all

4 papers · 1 filter

math.CO2016★ 2 cited

There are asymptotically the same number of Latin squares of each parity

Nicholas J. Cavenagh, Ian M. Wanless

A Latin square is reduced if its first row and column are in natural order. For Latin squares of a particular order $n$ there are four possible different parities. We confirm a con…

math.CO2016

Latin squares with no transversals

Nicholas J. Cavenagh, Ian M. Wanless

A $k$ -plex in a latin square of order $n$ is a selection of $k n$ entries that includes $k$ representatives from each row and column and $k$ occurrences of each symbol. A $1$ -plex i…

math.CO2016

Orthogonal trades in complete sets of MOLS

Nicholas J. Cavenagh, Diane M. Donovan, Fatih Demirkale

Let $B_{p}$ be the Latin square given by the addition table for the integers modulo an odd prime $p$ . Here we consider the properties of Latin trades in $B_{p}$ which preserve orthogon…

math.CO2016

On the distances between Latin squares and the smallest defining set size

Nicholas Cavenagh, Reshma Ramadurai

In this note we show that for each Latin square $L$ of order $n \geq 2$ , there exists a Latin square $L^{'} \neq = L$ of order $n$ such that $L$ and $L^{'}$ differ in at most $8 n$ cel…