dc.contributor.author
Frick, Florian
dc.contributor.author
Superdock, Matt
dc.date.accessioned
2025-04-09T13:03:08Z
dc.date.available
2025-04-09T13:03:08Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/47261
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-46979
dc.description.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.
en
dc.format.extent
16 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Simplicial complex
en
dc.subject
fundamental group
en
dc.subject
incidence geometry
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
Vertex numbers of simplicial complexes with free abelian fundamental group
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
P105
dcterms.bibliographicCitation.doi
10.26493/1855-3974.3089.b49
dcterms.bibliographicCitation.journaltitle
Ars Mathematica Contemporanea
dcterms.bibliographicCitation.number
1
dcterms.bibliographicCitation.volume
25
dcterms.bibliographicCitation.url
https://doi.org/10.26493/1855-3974.3089.b49
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik

refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
1855-3974
refubium.resourceType.provider
WoS-Alert