20.500.12556/RUP-21770 Vertex numbers of simplicial complexes with free abelian fundamental group Števila točk simplicialnih kompleksov s prosto abelsko fundamentalno grupo 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. simplicial complex fundamental group incidence geometry simplicialni komplels fundamentalna grupa incidenčna geometrija true false false Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-09-17 11:44:20 2025-09-18 10:41:09 2026-02-03 10:22:43 0000-00-00 00:00:00 2025 0 0 16 str. no. 1, [article no.] P1.05 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-02-13 51 1855-3974 10.26493/1855-3974.3089.b49 AMC_Superdock,Frick_2025.pdf AMC_Superdock,Frick_2025.pdf 1 FB1AE621997DB2C459DC14E1E76E80B2 c32e44d0669d82819f350b755edf24ca3b60f3e00c335ead612c2e19311910b3 143f2438-93ab-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31640 https://amc-journal.eu/index.php/amc/article/view/3089 1 fde047c2-93aa-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31639 Fakulteta za matematiko, naravoslovje in informacijske tehnologije Založba Univerze na Primorskem 0 0 0