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  "body": "\n## Statement\n\nIn mathematics, **Szymanski's conjecture**, named after Ted H. Szymanski, states that every [[permutation|05RWFKVTJ7]] on the $n$-dimensional doubly [[directed|0KFYGSHHF5]] hypercube graph can be routed with edge-disjoint [[paths|03NAMV1DHJ]]. That is, if the permutation $\\sigma$ matches each vertex $v$ to another vertex $\\sigma(v)$, then for each $v$ there exists a path in the hypercube graph from $v$ to $\\sigma(v)$ such that no two paths for two different vertices $u$ and $v$ use the same edge in the same direction.\n",
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        "what": "edge uses out",
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