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Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P-2-irreducible 3-manifold triangulations. In particular, new constraints are proven for face-pairing graphs, and pruning techniques are improved using a modification of the union-find algorithm. Using these results we catalogue all 136 closed non-orientable P-2-irreducible 3-manifolds that can be formed from at most 10 tetrahedra
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