Existence conditions for k- barycentric Olson constant
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| Авторы: | , , , |
|---|---|
| Формат: | artículo original |
| Статус: | Versión publicada |
| Дата публикации: | 2020 |
| Описание: | Let (G, +) be a finite abelian group and 3 ≤ k ≤ |G| a positive integer. The k-barycentric Olson constant denoted by BO(k, G) is defined as the smallest integer ℓ such that each set A of G with |A| = ℓ contains a subset with k elements {a1, . . . , ak} satisfying a1 + · · · + ak = kaj for some 1 ≤ j ≤ k. We establish some general conditions on G assuring the existence of BO(k, G) for each 3 ≤ k ≤ |G|. In particular, from our results we can derive the existence conditions for cyclic groups and for elementary p-groups p ≥ 3. We give a special treatment over the existence condition for the elementary 2-groups. |
| Страна: | Portal de Revistas UCR |
| Институт: | Universidad de Costa Rica |
| Repositorio: | Portal de Revistas UCR |
| Язык: | Inglés Español |
| OAI Identifier: | oai:portal.ucr.ac.cr:article/33773 |
| Online-ссылка: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/33773 |
| Access Level: | acceso abierto |
| Ключевое слово: | finite abelian group zero-sum problem baricentric-sum problem Davenport constant k-barycentric Olson constant grupos abelianos finitos problemas de suma-cero problemas de suma baricéntricas constante de Davenport constante k-baricéntrica de Olson |