Autor segons l'article: Garcia-Colin, N; Montejano, LP; Alfonsin, JLR
Departament: Enginyeria Informàtica i Matemàtiques
Autor/s de la URV: Montejano Cantoral, Luis Pedro
Paraules clau: Proof Cells Arrangements
Resum: 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.
Àrees temàtiques: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
Adreça de correu electrònic de l'autor: luispedro.montejano@urv.cat
Data d'alta del registre: 2024-08-03
Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
Referència a l'article segons font original: Mathematika. 69 (2): 535-561
Referència de l'ítem segons les normes 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
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2023
Tipus de publicació: Journal Publications
Repositori URV