Abstract

CAICEDO, Yadira; MARTOS O., Carlos A.  and  TRUJILLO S., Carlos A.. Constructions of Bh Sets in Various Dimensions. Ciencia en Desarrollo [online]. 2021, vol.12, n.2, pp.73-81.  Epub Jan 29, 2022. ISSN 0121-7488.  https://doi.org/10.19053/01217488.v12.n2.2021.12732.

Let A c Z+ and h be positive integer. We say that A is a Bh set if any integer n 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.

Keywords : B_h Set; B₂ Set; Field extension.

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