Author, as appears in the article.: Garcia-Colin, N; Montejano, LP; Alfonsin, JLR
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Montejano Cantoral, Luis Pedro
Keywords: Proof Cells Arrangements
Abstract: Let X be a set of n points in Rd$\mathbb {R}<^>d$ in general position. What is the maximum number of vertices that conv(T(X))$\mathsf {conv}(T(X))$ can have among all the possible permissible projective transformations T? In this paper, we investigate this and other related questions. After presenting several upper bounds, obtained by using oriented matroid machinery, we study a closely related problem (via Gale transforms) concerning the maximal number of minimal Radon partitions of a set of points. The latter led us to a result supporting a positive answer to a question of Pach and Szegedy asking whether balanced 2-colorings of points in the plane maximize the number of induced multicolored Radon partitions. We also discuss a related problem concerning the size of topes in arrangements of hyperplanes as well as a tolerance-type problem of finite sets.
Thematic Areas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: luispedro.montejano@urv.cat
Record's date: 2024-08-03
Papper version: info:eu-repo/semantics/publishedVersion
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Mathematika. 69 (2): 535-561
APA: Garcia-Colin, N; Montejano, LP; Alfonsin, JLR (2023). On the number of vertices of projective polytopes. Mathematika, 69(2), 535-561. DOI: 10.1112/mtk.12193
Entity: Universitat Rovira i Virgili
Journal publication year: 2023
Publication Type: Journal Publications
Repositori URV