Embedding Divisor and Semi-Prime Testability in f-vectors of polytopes
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We obtain computational hardness results for f-vectors of polytopes by exhibiting reductions of the problems DIVISOR and SEMI-PRIME TESTABILITY to problems on f-vectors of polytopes. Further, we show that the corresponding problems for f-vectors of simplicial polytopes are polytime solvable. The regime where we prove this computational difference (conditioned on standard conjectures on the density of primes and on P≠ NP) is when the dimension d tends to infinity and the number of facets is linear in d.
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