22 citations · 214 across the 59 of their papers we have counts for
7 papers · 1 filter
Parity of transversals of Latin squares
Darcy Best, Ian M. Wanless
We introduce a notion of parity for transversals, and use it to show that in Latin squares of order , the number of transversals is a multiple of 4. We also demonstrate…
Mutually orthogonal binary frequency squares
Thomas Britz, Nicholas J. Cavenagh, Adam Mammoliti +1
A \emph{frequency square} is a matrix in which each row and column is a permutation of the same multiset of symbols. We consider only {\em binary} frequency squares of order wi…
Maximally nonassociative quasigroups via quadratic orthomorphisms
Ales Drapal, Ian M. Wanless
A quasigroup is called maximally nonassociative if for we have that only if . We show that, with finitely many excep…
Small Latin arrays have a near transversal
Darcy Best, Kyle Pula, Ian M. Wanless
A Latin array is a matrix of symbols in which no symbol occurs more than once within a row or within a column. A diagonal of an array is a selection of cells taken…
Latin squares with maximal partial transversals of many lengths
Anthony B. Evans, Adam Mammoliti, Ian Wanless
A partial transversal of a Latin square is a set of entries of in which each row, column and symbol is represented at most once. A partial transversal is maximal if it…
Most binary matrices have no small defining set
Carly Bodkin, Anita Liebenau, Ian M. Wanless
Consider a matrix chosen uniformly at random from a class of matrices of zeros and ones with prescribed row and column sums. A partially filled matrix is a $\m…