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 constru...
- Autores:
- Tipo de recurso:
- 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
- Rights
- License
- http://purl.org/coar/access_right/c_abf2
| Summary: | 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. |
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