K. O'Bryant

activity

20022026

most citedConstructions of Generalized Sidon Sets

26 citations · 89 across the 23 of their papers we have counts for

collaborators

33 papers

math.CO2026

On the Thickness of Infinite Generalized Sidon Sets, II

Kevin O'Bryant

A set $A$ of nonnegative integers is a $B_{h}$ -set if the sums $a_{1} + \dots + a_{h}$ with $a_{1} \leq \dots \leq a_{h}$ and $a_{i} \in A$ are distinct; a $B_{2}$ -set is a Sidon set.…

math.CO2026

On the Thickness of Infinite Generalized Sidon Sets, I

Kevin O'Bryant

Let $g \geq 1$ . A set $A$ of nonnegative integers is a Sidon set if for each $d > 0$ there is at most one pair $(a, b) \in A \times A$ with $d = a - b$ . If the…

math.NT2023★ 1 cited

The fourth positive element in the greedy $B_{h}$ -set

Melvyn B. Nathanson, Kevin O'Bryant

For $h \geq 1$ , a $B_{h}$ -set is a set of integers such that every integer $n$ has at most one representation in the form $n = a_{i_{1}} + \dots + a_{i_{h}}$ , where $a_{i_{r}} \in A$ for…

math.NT2023★ 1 cited

Constructing Thick $B_{h}$ -sets

Kevin O'Bryant

A subset $A$ of a commutative semigroup $X$ is called a $B_{h}$ set in $X$ if the only solutions to $a_{1} + \dots + a_{h} = b_{1} + \dots + b_{h}$ (with $a_{i}, b_{i} \in A$ ) are the trivial solutio…

math.NT2022★ 2 cited

On the size of finite Sidon sets

Kevin O'Bryant

A Sidon set is a set of integers containing no nontrivial solutions to the equation $a + b = c + d$ . We improve on the lower bound on the diameter of a Sidon set with $k$ elements: if $k…

math.CO2022

Counting Dope Matrices

Noga Alon, Noah Kravitz, Kevin O'Bryant

For a polynomial $P$ of degree $n$ and an $m$ -tuple $Λ = (λ_{1}, \dots, λ_{m})$ of distinct complex numbers, the dope matrix of $P$ with respect to $Λ$ is $D_P(Λ)=(δ_{ij})_{i\in [1,m],j\in…

On the Thickness of Infinite Generalized Sidon Sets, II

On the Thickness of Infinite Generalized Sidon Sets, I

The fourth positive element in the greedy Bh​-set

Constructing Thick Bh​-sets

On the size of finite Sidon sets

Counting Dope Matrices

The fourth positive element in the greedy $B_{h}$ -set

Constructing Thick $B_{h}$ -sets