On Packing Densities of Set Partitions

TL;DR

This paper investigates the packing densities of set partitions, extending known results from permutations and words, and determines the packing density for a specific set partition.

Contribution

It generalizes packing density results to set partitions and computes the density for a particular partition not previously analyzed.

Findings

Provides packing densities for most partitions of {1,2,3}

Determines the packing density of the partition {{1,3},{2}}

Extends permutation and word packing density results to set partitions

Abstract

We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results give us most of the packing densities for partitions of the set $\{1,2,3\}$. In the final section we determine the packing density of the set partition $\{\{1,3\},\{2\}\}$.