发表机构
Lehman College (CUNY)（莱曼学院（市立大学系统））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对整数区间内最大Δ-分离西顿集的基数，推导了其上下界，属于加法数论中西顿集相关的理论研究。
AI 中文摘要
非空整数集A是Δ-分离的，当且仅当对A中任意不相等的元素a、a'，满足|a - a'| ≥ Δ。若和集hA中的每个元素都能唯一表示为A中h个元素的和，则称A为Bₕ集，B₂集也叫西顿集。本文针对整数区间{1,2,…,n}中最大的Δ-分离西顿集的基数，给出了上界与下界。
英文摘要
The set $A$ is a $B_h$-set if every element of the sumset $hA$ has a unique representation as a sum of $h$ elements of $A$. A $B_2$-set is also called a Sidon set. A $B_{h,Δ}$-set is a $B_h$-set $A$ whose sumset $hA$ is $Δ$-separated, that is, $|x-x'| \geq Δ$ for all $x,x' \in hA$ with $x\neq x'$. Upper and lower bounds are obtained for the cardinality of the largest $B_{2,Δ}$-sets contained in $\{1,2,\ldots, n\}$, that is, sets $A \subseteq \{1,2,\ldots, n\}$ such that, if $a,b,c,d \in A$ and $\{a,b\} \neq \{c,d\}$, then $|(a+b)-(c+d)| \geq Δ$.
CommentsRevised and improved with new open problems; 11 pages
