Benedict Randall Shaw

works on

canonical ramsey theory 1 cuboids 1 products of simplices 1 ramsey theory 1 simplices 1

From the 1 of 8 linked papers with an AI index.

activity

20242026

collaborators

8 papers

math.CO2026

Products of simplices are canonically Ramsey

Benedict Randall Shaw

The paper proves that any product of simplices is canonically Ramsey, meaning that for any coloring of a suitable point set, one can find either a monochromatic or a rainbow copy o…

math.CO2026

Cuboids are canonically Ramsey

Benedict Randall Shaw

We say a set of points $C \subset R^{n}$ is canonically Ramsey if there is some set of points $S \subset R^{n^{'}}$ such that any colouring of $S$ , with any number of co…

math.CO2025

Counterexamples to conjectures on strong maximality and minimality

Lawrence Hollom, Benedict Randall Shaw

We provide counterexamples to several conjectures concerning strongly maximal and strongly minimal structures in infinite graphs and hypergraphs. In particular, we construct 3-unif…

math.CO2025

New optima for the deletion shadow

Benedict Randall Shaw

For a family $F$ of words of length $n$ drawn from an alphabet $A = [r] = {1, \dots, r}$ , Danh and Daykin defined the deletion shadow $I^ F$ as the family containing…

math.CO2025

Connecting hypercube 1-factors

Lawrence Hollom, Benedict Randall Shaw

A 1-factorisation of a regular graph $G$ is a partition of its edge set $E (G)$ into perfect matchings of $G$ . Behague asked for the minimal $r = r (d)$ such that some $1$ -factorisatio…

math.CO2025

Minimal hypergraph non-jumps

Benedict Randall Shaw

An $r$ -uniform hypergraph, or $r$ -graph, has density $∣ E (G) ∣/∣ V (G)^{(r)} ∣$ . We say $I^\pm$ is a jump for $r$ -graphs if there is some constant $I^´ = I^´ (I^\pm)$ such that, for each $\varepsi…