Czédli Gábor; Kincses János: Representing convex geometries by almost-circles. In: Acta scientiarum mathematicarum, (83) 3-4. pp. 393-414. (2017)
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Absztrakt (kivonat)
Finite convex geometries are combinatorial structures. It follows from a recent result of M. Richter and L. G. Rogers that there is an infinite set TRR of planar convex polygons such that TRR with respect to geometric convex hulls is a locally convex geometry and every finite convex geometry can be represented by restricting the structure of TRR to a finite subset in a natural way. For a (small) nonnegative ǫ < 1, a differentiable convex simple closed planar curve S will be called an almost-circle of accuracy 1 − ǫ if it lies in an annulus of radii 0 < r1 ≤ r2 such that r1/r2 ≥ 1 − ǫ. Motivated by Richter and Rogers’ result, we construct a set Tnew such that (1) Tnew contains all points of the plane as degenerate singleton circles and all of its non-singleton members are differentiable convex simple closed planar curves; (2) Tnew with respect to the geometric convex hull operator is a locally convex geometry; (3) Tnew is closed with respect to non-degenerate affine transformations; and (4) for every (small) positive ǫ ∈ R and for every finite convex geometry, there are continuum many pairwise affine-disjoint finite subsets E of Tnew such that each E consists of almost-circles of accuracy 1 − ǫ and the convex geometry in question is represented by restricting the convex hull operator to E. The affine-disjointness of E1 and E2 means that, in addition to E1 ∩ E2 = ∅, even ψ(E1) is disjoint from E2 for every non-degenerate affine transformation ψ.
| Mű típusa: | Cikk, tanulmány, mű |
|---|---|
| Befoglaló folyóirat/kiadvány címe: | Acta scientiarum mathematicarum |
| Dátum: | 2017 |
| Kötet: | 83 |
| Szám: | 3-4 |
| ISSN: | 0001-6969 |
| Oldalak: | pp. 393-414 |
| Nyelv: | angol |
| Közreműködők: | Közreműködés Név NEM RÉSZLETEZETT Hajnal P. |
| Kiadó: | Bolyai Institute, University of Szeged |
| Kiadás helye: | Szeged |
| Hivatalos webcím (URL): | http://www.acta.hu |
| Befoglaló mű URL: | http://acta.bibl.u-szeged.hu/50020/ |
| DOI: | 10.14232/actasm-016-044-8 |
| Kulcsszavak: | Geometria - konvex, Matematika |
| Megjegyzések: | Bibliogr.: p. 413-414. ; ill. ; összefoglalás angol nyelven |
| Szakterület: | 01. Természettudományok 01. Természettudományok > 01.01. Matematika |
| Feltöltés dátuma: | 2018. feb. 09. 21:38 |
| Utolsó módosítás: | 2026. feb. 24. 08:10 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/50043 |
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