Go up to 7 Beyond PolytopesGo forward to 33 f-Vector of Simplicial Complexes |
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Input: | Finite abstract simplicial complex Δ given by a list
of facets |
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Output: | Euler characteristic χ(Δ) ∈ Z |

Status (general): | Open |
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Status (fixed dim.): | Polynomial time |

It is unknown whether the decision version "χ(Δ) = 0?"
of this problem is in NP. The problem is easy if Δ is
given by a list of all of its simplices. For fixed dimension, one
can enumerate all simplices of Δ and compute the Euler
characteristic in polynomial time.
Currently the fastest way to compute the Euler characteristic is
to first generate (the Hasse diagram of) Furthermore, if computing |

Related problems: | 33 |
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