The number of k-arc acyclic subdigraphs in which every vertex can reach a fixed root is independent of the root, for any balanced digraph.
Computing the EHZ capacity is NP-hard
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
The Ekeland-Hofer-Zehnder capacity (EHZ capacity) is a fundamental symplectic invariant of convex bodies. We show that computing the EHZ capacity of polytopes is NP-hard. For this we reduce the feedback arc set problem in bipartite tournaments to computing the EHZ capacity of simplices.
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An equality for balanced digraphs
The number of k-arc acyclic subdigraphs in which every vertex can reach a fixed root is independent of the root, for any balanced digraph.