Richard Montgomery

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20232026

most citedA proof of the Ryser-Brualdi-Stein conjecture for large even

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3 citations · 4 across the 3 of their papers we have counts for

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math.CO2026

Poset dimension and maximum comparability degree

Carla Groenland, Richard Montgomery, Rajko Nenadov +1

In 1986, Füredi and Kahn showed that the dimension $dim (P)$ of any finite poset $P$ satisfies $dim (P) = O (d lo g^{2} d)$ , where $d$ is the maximum degree of the comparability graph…

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★ 1 cited

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…

math.CO2024

Packing the largest trees in the tree packing conjecture

Barnabás Janzer, Richard Montgomery

The famous tree packing conjecture of Gyárfás 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 $n$ -vertex…

math.CO2023★ 3 cited

A proof of the Ryser-Brualdi-Stein conjecture for large even $n$

Richard Montgomery

A Latin square of order $n$ is an $n$ by $n$ grid filled using $n$ symbols so that each symbol appears exactly once in each row and column. A transversal in a Latin square is a col…

Poset dimension and maximum comparability degree

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

Almost-full transversals in equi-n-squares

Packing the largest trees in the tree packing conjecture

A proof of the Ryser-Brualdi-Stein conjecture for large even n

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

A proof of the Ryser-Brualdi-Stein conjecture for large even $n$