Solution to a conjecture of Schmidt and Tuller on one-dimensional packings and coverings

TL;DR

This paper confirms a conjecture by Schmidt and Tuller regarding optimal packings and coverings of integers with three-point sets, and connects it to broader combinatorial problems.

Contribution

It proves the Schmidt and Tuller conjecture on integer packings and coverings and explores its implications in combinatorics.

Findings

Conjecture by Schmidt and Tuller confirmed.

Connections established with other combinatorial problems.

Provides a comprehensive solution to a longstanding problem.

Abstract

In 2008, Schmidt and Tuller stated a conjecture concerning optimal packing and covering of integers by translates of a given three-point set. In this note, we confirm their conjecture and relate it to several other problems in combinatorics.