Patrick A. Bennett

collaborators

3 papers

math.CO2025

Some progress on $t$ -tone coloring

Patrick Bennett, Jade Nichols

A $t$ -tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d - 1$ colors. In this note,…

math.CO2025

The Sunflower-Free Process

Patrick Bennett, Amanda Priestley

An $r$ -sunflower is a collection of $r$ sets such that the intersection of any two sets in the collection is identical. We analyze a random process which constructs a $w$ -uniform $…

math.CO2024

Asymptotically optimal constant weight codes with even distance

Patrick Bennett

A $q$ -ary code $C$ of length $n$ is a set of $n$ -dimensional vectors (code words) with entries in ${0, \dots, q - 1}$ . We say $C$ has constant weight $w$ if each code word has exa…

Some progress on t-tone coloring

The Sunflower-Free Process

Asymptotically optimal constant weight codes with even distance

Some progress on $t$ -tone coloring