Wyniki wyszukiwania

1

Note on a problem of Ruzsa

100%

Hegyvári N.

Acta Arithmetica

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1995

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tom 69

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nr 2

113-119

2

On the representation of integers as sums of distinct terms from a fixed set

100%

Hegyvári N.

Acta Arithmetica

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2000

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tom 92

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nr 2

99-104

3

Explicit constructions of extractors and expanders

63%

Hegyvári N., Hennecart F.

Acta Arithmetica

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2009

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tom 140

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nr 3

233-249

4

On the subset sums of exponential type sequences

51%

Chen Y.-G., Fang J.-H., Hegyvári N.

Acta Arithmetica

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2016

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tom 173

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nr 2

141-150

EN

For a sequence A ⊆ ℕ, let P(A) be the set of all sums of distinct terms taken from A. The sequence A is said to be complete if P(A) contains all sufficiently large integers. Let p > 1 be an integer. The following main results are proved: (a) Let $A_t = {a_1 ≤ ... ≤ a_t}$ be any sequence of positive integers (not necessarily distinct), $S_p = {p^i : i = 0, 1, ... }$ and $S_p A_t = {p^i a_j : i = 0, 1, ...; j = 1, ..., t}$. When t ≥ p-1, the sequence P(S_pA_t)$ has positive lower asymptotic density not less than $1/a_{p-1}$. The lower bounds p-1 and $1/a_{p-1}$ are both the best possible. (b) For any positive integer k, the sequence ${ p^i F_j : i = 0, 1, ... ; j = k, k+1, ..., n}$ is complete, where $F_j$ is the jth Fibonacci number and $n = p^2 F_{k+2p-1}^2$.

Ograniczanie wyników

4 Acta Arithmetica

4 Hegyvári N.

1 Chen Y.-G.

1 Fang J.-H.

1 Hennecart F.

1 2016

1 2009

1 2000

1 1995

Note on a problem of Ruzsa

On the representation of integers as sums of distinct terms from a fixed set

Explicit constructions of extractors and expanders

On the subset sums of exponential type sequences