Cube Designs |
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| Authors: | Václav Linek Leonard H Soicher Brett Stevens |
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| Institution: | 1. Department of Mathematics and Statistics University of Winnipeg, Winnipeg, Canada;2. School of Mathematical Sciences, Queen Mary University of London, UK;3. School of Mathematics and Statistics, Carleton University Ottawa, Canada |
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| Abstract: | A cube design of order v, or a CUBE(v), is a decomposition of all cyclicly oriented quadruples of a v‐set into oriented cubes. A CUBE(v) design is unoriented if its cubes can be paired so that the cubes in each pair are related by reflection through the center. A cube design is degenerate if it has repeated points on one of its cubes, otherwise it is nondegenerate. We show that a nondegenerate CUBE(v) design exists for all integers  , and that an unoriented nondegenerate CUBE(v) design exists if and only if  and  or  . A degenerate example of a CUBE(v) design is also given for each integer  . |
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| Keywords: | cube designs polyhedral designs |
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