On the Thickness of Infinite Generalized Sidon Sets, II

Abstract

A set $\mathcal{A}$ of nonnegative integers is a $B_h$-set if the sums $a_1+\cdots+a_h$ with $a_1\le\cdots\le a_h$ and $a_i\in\mathcal{A}$ are distinct; a $B_2$-set is a Sidon set. We prove that for every even $h$ and every $B_h$-set $\mathcal{A}$, \[ \liminf_{n\to\infty} \frac{ | \mathcal{A}\cap[0,n) | }{\sqrt[h]{n/\log n}} \le \left(\fracπ{\log 2} \cdot \frac{Γ(1+h/2)^2}{Γ(1+1/h)^{h}}\right)^{1/h}. \]

Disclosure

“Tool and computational resource disclosure This work was developed in interaction with Anthropic’s ClaudeAI, the Fable model. Algebra, calculus, and inequalities were checked with Wolfram’s Mathematica 14.3. Lamport’s LATEX was used both for typesetting and interacting with ClaudeAI. While the writing has been heavily influenced by Clau”

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Formatting or typesetting

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2026-08-23T19:07:36.507935Z

Structural counts