Vertex numbers of simplicial complexes with free abelian fundamental groupFrick, Florian (Avtor) Superdock, Matt (Avtor) simplicial complexfundamental groupincidence geometryWe 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.Založba Univerze na Primorskem20252025-09-17 11:44:20Članek v reviji21770UDK: 51eISSN: 1855-3974DOI: 10.26493/1855-3974.3089.b49sl