[كتاب][B] Additive combinatorics
Additive combinatorics is the theory of counting additive structures in sets. This theory has
seen exciting developments and dramatic changes in direction in recent years thanks to its …
seen exciting developments and dramatic changes in direction in recent years thanks to its …
A complete annotated bibliography of work related to Sidon sequences
arxiv:math/0407117v1 [math.NT] 8 Jul 2004 A Complete Annotated Bibliography of Work
Related to Sidon Sequences Page 1 arxiv:math/0407117v1 [math.NT] 8 Jul 2004 A Complete …
Related to Sidon Sequences Page 1 arxiv:math/0407117v1 [math.NT] 8 Jul 2004 A Complete …
Generalized sidon sets
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the
property that the representation function is bounded by a prescribed number. We then use …
property that the representation function is bounded by a prescribed number. We then use …
On the order of magnitude of Sudler products
Given an irrational number $\alpha\in (0, 1) $, the Sudler product is defined by $ P_N
(\alpha)=\prod_ {r= 1}^{N} 2|\sin\pi r\alpha| $. Answering a question of Grepstad, Kaltenb\" …
(\alpha)=\prod_ {r= 1}^{N} 2|\sin\pi r\alpha| $. Answering a question of Grepstad, Kaltenb\" …
Upper and lower bounds for finite Bh [g] sequences
We give a non-trivial upper bound for Fh (g, N), the size of a Bh [g] subset of {1,…, N}, when
g> 1. In particular, we prove F2 (g, N)⩽ 1.864 (gN) 1/2+ 1, and F h (g, N)⩽ 1 (1+ cos h (π/h)) …
g> 1. In particular, we prove F2 (g, N)⩽ 1.864 (gN) 1/2+ 1, and F h (g, N)⩽ 1 (1+ cos h (π/h)) …
Constructions of generalized Sidon sets
We give explicit constructions of sets S with the property that for each integer k, there are at
most g solutions to k= s1+ s2, si∈ S; such sets are called Sidon sets if g= 2 and generalized …
most g solutions to k= s1+ s2, si∈ S; such sets are called Sidon sets if g= 2 and generalized …
Upper and lower bounds on the size of sets
A subset $ A $ of the integers is a $ B_k [g] $ set if the number of multisets from $ A $ that
sum to any fixed integer is at most $ g $. Let $ F_ {k, g}(n) $ denote the maximum size of a …
sum to any fixed integer is at most $ g $. Let $ F_ {k, g}(n) $ denote the maximum size of a …
New upper bounds for finite Bh sequences
Let Fh (N) be the maximum number of elements that can be selected from the set {1,…, N}
such that all the sums a1+…+ ah, a1⩽…⩽ ah are different. We introduce new combinatorial …
such that all the sums a1+…+ ah, a1⩽…⩽ ah are different. We introduce new combinatorial …
On extreme values for the Sudler product of quadratic irrationals
Given a real number $\alpha $ and a natural number $ N $, the Sudler product is defined by
$ P_N (\alpha)=\prod_ {r= 1}^{N} 2\left\lvert\sin (\pi\left (r\alpha\right))\right\rvert. $ Denoting …
$ P_N (\alpha)=\prod_ {r= 1}^{N} 2\left\lvert\sin (\pi\left (r\alpha\right))\right\rvert. $ Denoting …
The number of B3-sets of a given cardinality
A set S of integers is a B 3-set if all the sums of the form a 1+ a 2+ a 3, with a 1, a 2 and a 3∈
S and a 1≤ a 2≤ a 3, are distinct. We obtain asymptotic bounds for the number of B 3-sets …
S and a 1≤ a 2≤ a 3, are distinct. We obtain asymptotic bounds for the number of B 3-sets …