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30
A note on Freiman’s theorem in vector spaces
 COMBINATORICS, PROBABILITY AND COMPUTING
, 2006
"... A famous result of Freiman describes the sets A, of integers, for which A + A  ≤ KA. In this short note we address the analagous question for subsets of vector spaces over F2. Specifically we show that if A is a subset of a vector space over F2 with A + A  ≤ KA  then A is contained in a c ..."
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Cited by 10 (3 self)
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A famous result of Freiman describes the sets A, of integers, for which A + A  ≤ KA. In this short note we address the analagous question for subsets of vector spaces over F2. Specifically we show that if A is a subset of a vector space over F2 with A + A  ≤ KA  then A is contained in a
FreimanRuzsaType Theory For Small Doubling Constant
, 805
"... In this paper, we study the linear structure of sets A ⊂ Fn 2 with doubling constant σ(A) < 2, where σ(A): = A+A A. In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with V  ≤ A. Finally, we ..."
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In this paper, we study the linear structure of sets A ⊂ Fn 2 with doubling constant σ(A) < 2, where σ(A): = A+A A. In particular, we show that A is contained in a small affine subspace. We also show that A can be covered by at most four shifts of some subspace V with V  ≤ A. Finally
Sets with small sumset and rectification
 BULL. LONDON MATH. SOC
, 2005
"... We study the extent to which sets A ⊆ Z/NZ, N prime, resemble sets of integers from the additive point of view (“up to Freiman isomorphism”). We give a direct proof of a result of Freiman, namely that if A+A  � KA  and A  < c(K)N then A is Freiman isomorphic to a set of integers. Because ..."
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Cited by 27 (7 self)
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we avoid appealing to Freiman’s structure theorem, we get a reasonable bound: we can take c(K) � (32K) −12K2. As a byproduct of our argument we obtain a sharpening of the second author’s result on, and if A+A  � KA, sets with small sumset in torsion groups. For example if A ⊆ Fn 2 then A
The number of maximal sumfree subsets of integers
, 2014
"... Cameron and Erdős [6] raised the question of how many maximal sumfree sets there are in {1,..., n}, giving a lower bound of 2bn/4c. In this paper we prove that there are in fact at most 2(1/4+o(1))n maximal sumfree sets in {1,..., n}. Our proof makes use of container and removal lemmas of Green [ ..."
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Cited by 1 (1 self)
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[8, 9] as well as a result of Deshouillers, Freiman, Sós and Temkin [7] on the structure of sumfree sets. 1
A STRUCTURAL APPROACH TO SUBSETSUM PROBLEMS
, 2008
"... We discuss a structural approach to subsetsum problems in additive combinatorics. The core of this approach are Freimantype structural theorems, many of which will be presented through the paper. These results have applications in various areas, such as number theory, combinatorics and mathematica ..."
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We discuss a structural approach to subsetsum problems in additive combinatorics. The core of this approach are Freimantype structural theorems, many of which will be presented through the paper. These results have applications in various areas, such as number theory, combinatorics
Sharp bound on the number of maximal sumfree subsets of integers
, 2015
"... Cameron and Erdős [6] asked whether the number of maximal sumfree sets in {1,..., n} is much smaller than the number of sumfree sets. In the same paper they gave a lower bound of 2bn/4c for the number of maximal sumfree sets. Here, we prove the following: For each 1 ≤ i ≤ 4, there is a constant ..."
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Cited by 3 (2 self)
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Ci such that, given any n ≡ i mod 4, {1,..., n} contains (Ci + o(1))2 n/4 maximal sumfree sets. Our proof makes use of container and removal lemmas of Green [10, 11], a structural result of Deshouillers, Freiman, Sós and Temkin [7] and a recent bound on the number of subsets of integers with small
On the Rate of Decay of the Concentration Function of the Sum of Independent Random Variables
, 2003
"... Abstract. Let X1,..., Xn be i.i.d. integral valued random variables and Sn their sum. In the case when X1 has a moderately large tail of distribution, Deshouillers, Freiman and Yudin gave a uniform upper bound for maxk∈Z Pr{Sn = k} (which can be expressed in term of the Lévy Doeblin concentration o ..."
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Abstract. Let X1,..., Xn be i.i.d. integral valued random variables and Sn their sum. In the case when X1 has a moderately large tail of distribution, Deshouillers, Freiman and Yudin gave a uniform upper bound for maxk∈Z Pr{Sn = k} (which can be expressed in term of the Lévy Doeblin concentration
REFINED BOUND FOR SUMFREE SETS IN GROUPS OF PRIME ORDER
, 705
"... Abstract. Improving upon earlier results of Freiman and the present authors, we show that if p is a sufficiently large prime and A is a sumfree subset of the group of order p, such that n: = A > 0.318p, then A is contained in a dilation of the interval [n, p − n] (mod p). 1. ..."
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Cited by 1 (0 self)
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Abstract. Improving upon earlier results of Freiman and the present authors, we show that if p is a sufficiently large prime and A is a sumfree subset of the group of order p, such that n: = A > 0.318p, then A is contained in a dilation of the interval [n, p − n] (mod p). 1.
On the critical pair theory in abelian groups: Beyond Chowla’s Theorem
, 2007
"... We obtain critical pair theorems for subsets S and T of an abelian group such that S + T  ≤ S  + T . We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rødseth and one of the authors. 1 ..."
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Cited by 3 (3 self)
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We obtain critical pair theorems for subsets S and T of an abelian group such that S + T  ≤ S  + T . We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rødseth and one of the authors. 1
The EisenbudKohStillman Conjecture on
 Linear Syzygies, Invent. Math
, 1999
"... A subset A of the integers is said to be sumfree if there do not exist elements x,y,z ∈ A with x+y = z. It is shown that the number of sumfree subsets of {1,...,N} is O(2 N/2), confirming a wellknown conjecture of Cameron and Erdős. 1. Introduction. If A is any subset of an abelian group then we ..."
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Cited by 21 (2 self)
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A subset A of the integers is said to be sumfree if there do not exist elements x,y,z ∈ A with x+y = z. It is shown that the number of sumfree subsets of {1,...,N} is O(2 N/2), confirming a wellknown conjecture of Cameron and Erdős. 1. Introduction. If A is any subset of an abelian group then we
Results 1  10
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