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- In mathematics, Szymanski's conjecture, named after Ted H. Szymanski, states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths. That is, if the permutation σ matches each vertex v to another vertex σ(v), then for each v there exists a path in the hypercube graph from v to σ(v) such that no two paths for two different vertices u and v use the same edge in the same direction. Through computer experiments it has been verified that the conjecture is true for n ≤ 4. Although the conjecture remains open for n ≥ 5, in this case there exist permutations that require the use of paths that are not shortest paths in order to be routed. (en)
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- 2094 (xsd:nonNegativeInteger)
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- In mathematics, Szymanski's conjecture, named after Ted H. Szymanski, states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths. That is, if the permutation σ matches each vertex v to another vertex σ(v), then for each v there exists a path in the hypercube graph from v to σ(v) such that no two paths for two different vertices u and v use the same edge in the same direction. (en)
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- Szymanski's conjecture (en)
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