Embedding Divisor and Semi-Prime Testability in f-Vectors of Polytopes

Eran Nevo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 situation 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.

Original languageAmerican English
Pages (from-to)297-303
Number of pages7
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - Jul 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Computational complexity
  • Polytopes
  • f-vector


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