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Multiple recurrence and nilsequences
- V. Bergelson, B. Host, Bryna Kra, I. Ruzsa
- Mathematics
- 1 March 2005
Aiming at a simultaneous extension of Khintchine’s and Furstenberg’s Recurrence theorems, we address the question if for a measure preserving system $(X,\mathcal{X},\mu,T)$ and a set…
Solving a linear equation in a set of integers I
- I. Ruzsa
- Mathematics
- 1993
(1.1) a1x1 + . . .+ akxk = b with x1, . . . , xk in a prescribed set of integers. We saw that the vanishing of the constant term b and the sum of coefficients s = a1 + . . . + ak had a strong effect…
Freiman's theorem in an arbitrary abelian group
A famous result of Freiman describes the structure of finite sets A ⊆ ℤ with small doubling property. If |A + A| ⩽ K|A|, then A is contained within a multidimensional arithmetic progression of…
Generalized arithmetical progressions and sumsets
- I. Ruzsa
- Mathematics
- 1 December 1994
Sum-free sets in abelian groups
LetA be a subset of an abelian groupG with |G|=n. We say thatA is sum-free if there do not existx, y, z εA withx+y=z. We determine, for anyG, the maximal densityμ(G) of a sum-free subset ofG. This…
An analog of Freiman's theorem in groups
- I. Ruzsa
- Mathematics
- 1993
It is proved that any set A in a commutative group G where the order of elements is bounded by an integer r having n elements and at most n sums is contained in a subgroup of size An with A = f(r; )…
An Infinite Sidon Sequence
- I. Ruzsa
- Mathematics
- 1998
Abstract We show the existence of an infinite Sidon sequence such that the number of elements in [1, N ] is N 2 −1+ o (1) for all large N .
Convexity and Sumsets
- G. Elekes, M. Nathanson, I. Ruzsa
- Mathematics
- 1 August 2000
Difference sets and frequently hypercyclic weighted shifts
Abstract We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on ${\ell }^{p} ( \mathbb{Z} )$, $p\geq 1$. Our method uses…
Adding Distinct Congruence Classes Modulo a Prime
- N. Alon, M. Nathanson, I. Ruzsa
- Mathematics
- 1 March 1995
The Cauchy-Davenport theorem states that if A and B are nonempty sets of congruence classes modulo a prime p, and if |A| = k and |B| = l, then the sumset A + B contains at least min(p, k + l − 1)…
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