Richard Montgomery

activity

20242026

collaborators

3 papers

math.CO2026

Packing the largest trees in the tree packing conjecture

BarnabÃ¡s Janzer, Richard Montgomery

The famous tree packing conjecture of GyÃ¡rfÃ¡s from 1976 says that any sequence of trees $T_{1}, \dots, T_{n}$ such that $∣ T_{i} ∣ = i$ for each $i \in [n]$ packs into the complete $n$ -verte…

math.CO2025

Asymptotically-tight packing and covering with transversal bases in Rota's basis conjecture

Richard Montgomery, Lisa Sauermann

In 1989, Rota conjectured that, given any $n$ bases $B_{1}, \dots, B_{n}$ of a vector space of dimension $n$ , or more generally a matroid of rank $n$ , it is possible to rearrange these i…

math.CO2024

Almost-full transversals in equi- $n$ -squares

Debsoumya Chakraborti, Micha Christoph, Zach Hunter +2

In 1975, Stein made a wide generalisation of the Ryser-Brualdi-Stein conjecture on transversals in Latin squares, conjecturing that every equi- $n$ -square (an $n \times n$ array fill…

Packing the largest trees in the tree packing conjecture

Asymptotically-tight packing and covering with transversal bases in Rota's basis conjecture

Almost-full transversals in equi-n-squares

Almost-full transversals in equi- $n$ -squares