Additive bases without any essential subsets
Peter V. Hegarty · arXiv (Cornell University) · 2008
ABSTRACT. Let A be a basis for N0 of some order. By an essential subset of A one means a subset P such that A\\P is no longer a basis (of any order) and such that P is minimal among all subsets of A with this property. In a recent paper, Deschamps and Farhi asked whether every basis of N0 possesses some such subset. We construct, for every integer h ≥ 2, a basis of order h with no essential subsets. We also exhibit bases for Z without essential subsets. 1.