5 papers
Maximal sets of mutually orthogonal frequency squares
Nicholas J. Cavenagh, Adam Mammoliti, Ian M. Wanless
A frequency square is a square matrix in which each row and column is a permutation of the same multiset of symbols. A frequency square is of type if it contains symb…
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…
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…
The -matching sequencibility of complete multi--partite -graphs
Adam Mammoliti
Alspach [{\sl Bull. Inst. Combin. Appl.}~{\bf 52} (2008), 7--20] defined the maximal matching sequencibility of a graph , denoted~, to be the largest integer for whic…
Balanced diagonals in frequency squares
Nicholas Cavenagh, Adam Mammoliti
We say that a diagonal in an array is {\em -balanced} if each entry occurs times. Let be a frequency square of type ; that is, an array in which ea…