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- W1615448654 abstract "A_k = {1, a_2, ... a_k} is an h-basis for X if every positive integer not exceeding X can be expressed as the sum of no more than h values a_i; X(h) is called the h-range of the basis. h_0 is the smallest value of h for which X(h) is greater than or equal to a_k, and h_1 is the smallest value for which X(h+1) = X(h) + a_k for all h greater than or equal to h_1. h_2 identifies a further stabilisation in the h-range - a definition is included in the body of the paper. It is known that h_1 and h_2 do not exceed h_0 for h-bases A_3, but published proofs are complicated (see Ch. VIII of [4], where references [3] and [5] are given). This paper introduces the concept of a A = {1, a_2, a_3} which, while sharing some of the properties of a basis A_3, is simpler to treat mathematically. We establish a relationship between stride generators and h-bases, and show that the result follows immediately if the stride generator underlying a basis has a particular property - here called canonicality. The proof is lengthy (with a number of special cases to consider), but the underlying principles remain simple." @default.
- W1615448654 created "2016-06-24" @default.
- W1615448654 creator A5083991777 @default.
- W1615448654 date "2014-03-15" @default.
- W1615448654 modified "2023-09-27" @default.
- W1615448654 title "A proof that h_1, h_2 <= h_0 for any h-basis A_3" @default.
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- W1615448654 hasPublicationYear "2014" @default.
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