Autor según el artículo: Garcia-Colin, N; Montejano, LP; Alfonsin, JLR
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Montejano Cantoral, Luis Pedro
Palabras clave: Proof Cells Arrangements
Resumen: 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.
Áreas temáticas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
Direcció de correo del autor: luispedro.montejano@urv.cat
Fecha de alta del registro: 2024-08-03
Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Mathematika. 69 (2): 535-561
Referencia 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
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2023
Tipo de publicación: Journal Publications
Repositori URV