On Complementing Sets of Nonnegative Integers

Vaidya, A. M.

doi:10.1080/0025570x.1966.11975676

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C(n) = σ C(d) D\n1

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2020

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“…The structure of complementing pairs A and B has been studied by de Bruijn [1], [2], [3] for the cases C = I and C = N and by A. M. Vaidya [7] who reproduced a fundamental result of de Bruijn for the latter case. In case C = N it is easy to see that A Π B = {0} and that 1 e A U B.…”

Section: C(n) = σ C(d) D\nmentioning

confidence: 94%

Addition theorems for sets of integers

Long¹

1967

Pacific J. Math.

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Section: C(n) = σ C(d) D\nmentioning

confidence: 94%

Addition theorems for sets of integers

Long¹

1967

Pacific J. Math.

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“…The characterization of N-pairs is much easier and it was implicitly in the work of de Bruijn [2], and was rediscovered by Vaidya [16]. Let (n k ) k≥1 be a sequence of integers with n k ≥ 2.…”

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confidence: 99%

Characterization of complementing pairs of $({\mathbb Z}_{\geq 0})^n$

Rao,

Yang,

Zhang

2020

Preprint

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Let A, B, C be subsets of an abelian group G. A pair (A, B) is called a C-pair if A, B ⊂ C and C is the direct sum of A and B. The Z + -pairs are characterized by de Bruijn in 1950 and the (Z + ) 2 -pairs are characterized by Niven in 1971.In this paper, we characterize the (Z + ) n -pairs for all n ≥ 1. We show that every (Z + ) n -pair is characterized by a weighted tree if it is primitive, that is, it is not a Cartesian product of a (Z + ) p -pair and a (Z + ) q -pair of lower dimensions.

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On Complementing Sets of Nonnegative Integers

Cited by 2 publications

References 0 publications

Addition theorems for sets of integers

Addition theorems for sets of integers

Characterization of complementing pairs of $({\mathbb Z}_{\geq 0})^n$

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