11 papers
Latin Squares whose transversals intersect in unusual ways
Afsane Ghafari, Ian M. Wanless
A latin square of order is an array in which each of symbols occurs exactly once in each row and column. A transversal in such a square is a selection of en…
Latin hypercubes with restricted transversals
Billy Child, Ian M. Wanless
A -plane of a -dimensional array is a subarray formed by fixing coordinates and allowing the remaining coordinates to vary freely. A Latin hypercube of dimension $d…
Perfect -factorisations of
Jack Allsop, Ian M. Wanless
A perfect -factorisation of a graph is a decomposition of that graph into -factors such that the union of any two -factors is a Hamiltonian cycle. A Latin square of order…
A cube dismantling problem related to bootstrap percolation
János Barát, Ian M. Wanless
An hypercube is made from unit hypercubes. Two unit hypercubes are neighbours if they share a -dimensional face. In each step of a disma…
Autoparatopisms of Quasigroups and Latin Squares
Mahamendige Jayama Lalani Mendis, Ian M. Wanless
Paratopism is a well known action of the wreath product on Latin squares of order . A paratopism that maps a Latin square to itself is an autopar…
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…