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Globally simple Heffter arrays when
K. Burrage, Nicholas J. Cavenagh, D. Donovan +1
Square Heffter arrays are arrays such that each row and each column contains filled cells, each row and column sum is divisible by and either or ap…
Biembeddings of cycle systems using integer Heffter arrays
Nicholas J. Cavenagh, D. Donovan, E. Ş. Yazici
In this paper we will show the existence of a face -colourable biembedding of the complete graph onto an orientable surface where each face is a cycle of a fixed length , for…
Embedding partial Latin squares in Latin squares with many mutually orthogonal mates
Diane M. Donovan, Mike Grannell, Emine Şule Yazıcı
We show that any partial Latin square of order can be embedded in a Latin square of order at most which has at least mutually orthogonal mates. We also show that f…
The existence of square non-integer Heffter arrays
Nicholas J. Cavenagh, Jeff Dinitz, Diane Donovan +1
A Heffter array is an matrix such that each row and column contains filled cells, each row and column sum is divisible by and either or ap…
Enumerations of maximum partial triple systems on 16 and 17 points
Fatih Demirkale, Diane Donovan, Mike Grannell
For or 3 (mod 6), maximum partial triple systems on points are Steiner triple systems, STS()s. The 80 non-isomorphic STS(15)s were first enumerated around 100 ye…
A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs
Diane Donovan, Benjamin Haaland, David J. Nott
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, includ…