Richard Montgomery

activity

20202025

collaborators

4 papers

math.CO2025

Almost every Latin square has a decomposition into transversals

Candida Bowtell, Richard Montgomery

In 1782, Euler conjectured that no Latin square of order $n \equiv 2 mod 4$ has a decomposition into transversals. While confirmed for $n = 6$ by Tarry in 1900, Bose, Par…

math.CO2024

Transversals in Latin Squares

Richard Montgomery

A Latin square is an $n$ by $n$ grid filled with $n$ symbols so that each symbol appears exactly once in each row and each column. A transversal in a Latin square is a collection o…

math.DS2024

The negative energy N-body problem has finite diameter

Richard Montgomery

The Jacobi-Maupertuis metric provides a reformulation of the classical N-body problem as a geodesic flow on an energy-dependent metric space denoted $M_{E}$ where $E$ is the energy o…

math.CO2020

A proof of Ringel's Conjecture

Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov

A typical decomposition question asks whether the edges of some graph $G$ can be partitioned into disjoint copies of another graph $H$ . One of the oldest and best known conjectures…