1 citations · 1 across the 5 of their papers we have counts for
7 papers
Almost every Latin square has a decomposition into transversals
Candida Bowtell, Richard Montgomery
In 1782, Euler conjectured that no Latin square of order has a decomposition into transversals. While confirmed for by Tarry in 1900, Bose, Par…
Transversals in Latin Squares
Richard Montgomery
A Latin square is an by grid filled with symbols so that each symbol appears exactly once in each row and each column. A transversal in a Latin square is a collection o…
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 where is the energy o…
The Honest Embedding Dimension of a Numerical Semigroup
Richard Montgomery
Attached to a singular analytic curve germ in -space is a numerical semigroup: a subset of the non-negative integers which is closed under addition and whose complement isfi…
The Kepler Cone, Maclaurin Duality and Jacobi-Maupertuis metrics
Richard Montgomery
The Kepler problem is the special case of the power law problem: to solve Newton's equations for a central force whose potential is of the form where is a coupl…
A proof of Ringel's Conjecture
Richard Montgomery, Alexey Pokrovskiy, Benny Sudakov
A typical decomposition question asks whether the edges of some graph can be partitioned into disjoint copies of another graph . One of the oldest and best known conjectures…
Chaotic Geodesics in Carnot Groups
R. Montgomery, M. Shapiro, A. Stolin
The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corre…