Constructions of Bh sets in various dimensions

Let A ⊂ Z+ and h be positive integer.We say that A is a Bh set if any integern can be written in at most one-ways as the sum of h elements of A, The fundamental problem is to determine the cardinal maximum of a set Bh contained in the integer interval [1, n] := {1, 2, 3, . . . , n}. Not many constructions of integer sets Bh are known, among them are Singer [13], Bose-Chowla [3] and Gómez-Trujillo [7]. The Bh set concept can be extended to arbitrary groups. In this article, the generalized constructions on the groups that come from a field are presented and new construction of a set Bh+s in h + 1 dimensions is obtained.

• Fecha de publicación: 2021
• Institución: Universidad Pedagógica y Tecnológica de Colombia
• Repositorio: RiUPTC: Repositorio Institucional UPTC
• Idioma: spa
• OAI Identifier: oai:repositorio.uptc.edu.co:001/15318
• Acceso en línea: https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/12732; https://repositorio.uptc.edu.co/handle/001/15318
• Palabra clave: Conjunto $B_h$, Conjunto $B_2$, Extensión de campo; $B_h$ Set, $B_2$ Set, Field extension
• License: http://purl.org/coar/access_right/c_abf2