7 papers
Universal probability bounds for partial Latin squares
Jack Allsop, Patrick Morris
This paper studies the probability of substructures occurring in random Latin squares. Our main result states that if are such that , then there are positive co…
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…
Spanning Components and Surfaces Under Minimum Vertex Degree
Jack Allsop, Ander Lamaison, Richard Lang +1
We study minimum vertex-degree conditions in 3-uniform hypergraphs for (tight) spanning components and (combinatorial) surfaces. Our main results show that a 3-uniform hypergraph $…
Outline Rectangles, Allocations, and Latin Young Diagrams
Jack Allsop, Daniel Kotlar, Ian Wanless
A Young diagram is \emph{Latin} if there is an assignment of integers to its cells so that each row of length is populated by the numbers , and the numbers…
Isotopisms of quadratic quasigroups
Jack Allsop
A quasigroup is a pair where is a non-empty set and is a binary operation on such that for every there exists a unique $(x, y) \in Q^2…
Subsquares in random Latin rectangles
Jack Allsop, Ian M. Wanless
Suppose that is a function of and . We show that with probability , a uniformly random Latin rectangle contains no proper Latin subsquare…