Minimum packing density for sets of four integers

TL;DR

This paper proves that among all sets of four integers, the set {0, 1, 4, 6} has the lowest packing density of 1/7, establishing a minimal density result.

Contribution

It identifies the set {0, 1, 4, 6} as having the minimum packing density among all four-integer sets, providing a definitive density value.

Findings

Set {0, 1, 4, 6} achieves the minimum density of 1/7.

No other four-integer set has a lower packing density.

The result characterizes the optimal packing configuration for four-integer sets.

Abstract

We prove that the set $\{0, 1, 4, 6\}$ achieves the minimum packing density among all sets of integers with cardinality four, with a density of $\frac{1}{7}$.