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- W3204000283 abstract "We show that the minimum number of vertices of a simplicial complex with fundamental group ℤn is at most O(n) and at least Ω(n3/4). For the upper bound, we use a result on orthogonal 1-factorizations of K2n. For the lower bound, we use a fractional Sylvester–Gallai result. This application of extremal results in discrete geometry seems to be new. We also prove that any group presentation ⟨S|R⟩ ≅ ℤn whose relations are of the form gahbic for g, h, i ∈ S has at least Ω(n3/2) generators." @default.
- W3204000283 created "2021-10-11" @default.
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- W3204000283 date "2023-09-26" @default.
- W3204000283 modified "2023-10-01" @default.
- W3204000283 title "Vertex numbers of simplicial complexes with free abelian fundamental group" @default.
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- W3204000283 doi "https://doi.org/10.26493/1855-3974.3089.b49" @default.
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