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 cons...
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| Format: | Online |
| Language: | spa |
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Universidad Pedagógica y Tecnológica de Colombia
2021
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| Online Access: | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/12732 |
| _version_ | 1801706349844758528 |
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| author | Caicedo Bravo, Nidia Yadira Martos Ojeda, Carlos Andres Trujillo Solarte, Carlos Alberto |
| author_facet | Caicedo Bravo, Nidia Yadira Martos Ojeda, Carlos Andres Trujillo Solarte, Carlos Alberto |
| author_sort | Caicedo Bravo, Nidia Yadira |
| collection | OJS |
| description |
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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| format | Online |
| id | oai:oai.revistas.uptc.edu.co:article-12732 |
| institution | Revista Ciencia en Desarrollo |
| language | spa |
| publishDate | 2021 |
| publisher | Universidad Pedagógica y Tecnológica de Colombia |
| record_format | ojs |
| spelling | oai:oai.revistas.uptc.edu.co:article-127322022-06-15T16:53:13Z Constructions of Bh sets in various dimensions Construcción de conjuntos Bh en varias dimensiones Caicedo Bravo, Nidia Yadira Martos Ojeda, Carlos Andres Trujillo Solarte, Carlos Alberto Conjunto $B_h$, Conjunto $B_2$, Extensión de campo $B_h$ Set, $B_2$ Set, Field extension 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. Un conjunto Bh es un subconjunto A de números enteros con la propiedad que todas las sumas de h elementos son distintas, salvo permutaciones de los sumandos. El problema fundamental consiste en determinar el máximo cardinal de un conjunto Bh contenido en el intervalo entero [1, n] := {1, 2, 3, . . . , n}. Se conocen pocas construcciones de conjuntos Bh enteros, entre ellas se tienen la de Singer [13], Bose-Chowla [3] y Gómez-Trujillo [7]. El concepto de conjunto Bh se puede extender a grupos arbitrarios. En este articulo se presentan las construcciones generalizadas a los grupos que provienen de un cuerpo y se obtiene una nueva construcción de un conjunto Bh+s en h + 1 dimensiones. Universidad Pedagógica y Tecnológica de Colombia 2021-09-07 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Texto application/pdf https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/12732 10.19053/01217488.v12.n2.2021.12732 Ciencia En Desarrollo; Vol. 12 No. 2 (2021): Vol 12, Núm.2 (2021): Julio-Diciembre Ciencia en Desarrollo; Vol. 12 Núm. 2 (2021): Vol 12, Núm.2 (2021): Julio-Diciembre 2462-7658 0121-7488 spa https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/12732/11165 |
| spellingShingle | Conjunto $B_h$, Conjunto $B_2$, Extensión de campo $B_h$ Set, $B_2$ Set, Field extension Caicedo Bravo, Nidia Yadira Martos Ojeda, Carlos Andres Trujillo Solarte, Carlos Alberto Constructions of Bh sets in various dimensions |
| title | Constructions of Bh sets in various dimensions |
| title_alt | Construcción de conjuntos Bh en varias dimensiones |
| title_full | Constructions of Bh sets in various dimensions |
| title_fullStr | Constructions of Bh sets in various dimensions |
| title_full_unstemmed | Constructions of Bh sets in various dimensions |
| title_short | Constructions of Bh sets in various dimensions |
| title_sort | constructions of bh sets in various dimensions |
| topic | Conjunto $B_h$, Conjunto $B_2$, Extensión de campo $B_h$ Set, $B_2$ Set, Field extension |
| topic_facet | Conjunto $B_h$, Conjunto $B_2$, Extensión de campo $B_h$ Set, $B_2$ Set, Field extension |
| url | https://revistas.uptc.edu.co/index.php/ciencia_en_desarrollo/article/view/12732 |
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