# Long regularly-spaced and convex sequences in dense sets of integers

## TL;DR

This paper investigates the maximum length of regularly-spaced and convex integer sequences within dense sets and their differences, providing bounds that advance understanding of their structure.

## Contribution

It establishes new upper and lower bounds for the longest regularly-spaced and convex subsets in dense integer sets and their differences.

## Key findings

- Derived bounds for the longest such sequences in dense sets
- Extended results to the difference set A-A
- Enhanced understanding of structure in dense integer sets

## Abstract

Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.