Christopher Williamson

collaborators

4 papers

cs.CC2026

Secret Sharing at the Shannon Ceiling

Christopher Williamson

For every $n \geq 9$ that is a multiple of 3, we construct an explicit access structure on $n$ participants. In every perfect secret-sharing scheme realising this access structure,…

math.CO2026

Finite Three-Colourable (0,2)-Graphs Are Bipartite

Christopher Williamson

A theorem of Payan says that a cubelike graph cannot have chromatic number exactly three. A nearby question, usually discussed as Payan's finite $(0, 2)$ -graph question, asks whethe…

cs.CC2026

Symmetric Bounded Indistinguishability: Hypergeometric Smoothing and Hahn Polynomials

Christopher Williamson

A pair of probability distributions over ${0, 1}^{n}$ is said to be $(k, δ)$ -wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $δ$ . Prev…

math.HO2025

Extremal poker hand rankings: why the standard 52 card deck and a 3044 card deck are special

Christopher Williamson

We study poker hand rankings in the partially generalised setting of a deck with $r$ ranks, rather than the typical 13 ranks. We provide the hand rankings for all $r$ and observe s…