2008/07/22 by Bakir Farhi, Farhi, Bakir
Computer Science · Mathematics · #11B13 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11B13
paper · pdf · doi:10.48550/arxiv.0807.3461
3 pages
openalex publication_date 2008/07/22 · arxiv created 2008/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be an additive basis. We call ``essential subset'' of A any finite subset P of A such that A ∖ P is not an additive basis and that P is minimal (for the inclusion order) to have this property. A recent theorem due to B. Deschamps and the author states that any additive basis has only finitely many essential subsets (see ``Essentialité dans les bases additives, J. Number Theory, 123 (2007), p. 170-192''). The aim of this note is to give a simple proof of this theorem.