Vuong Bui

activity

20212025

collaborators

4 papers

math.CO2025

A short proof of an upper bound on the growth constant of polyiamonds

Vuong Bui

We provide a short and elementary proof that the growth constant of polyiamonds is at most $1 + 2 z + 3 z^{2}$ for the unique real root $z$ of the equation $2 z^{3} + z^{2} - 1 = 0$ . This coincidenta…

math.CO2025

A characterization of the Carathéodory number for $H$ -convexity

Vuong Bui

We show that the Carathéodory number for $H$ -convexity is the maximum of two parameters: the Helly number for $H$ -convexity and the cone number of $H$ . The cone number in this arti…

math.CO2024

Bounding Klarner's constant from above using a simple recurrence

Vuong Bui

Klarner and Rivest showed that the growth of the number of polyominoes, also known as Klarner's constant, is at most $2 + 22 < 4.83$ by viewing polyominoes as a sequence of twig…

math.CO2021

A characterization of strongly monotypic polytopes

Vuong Bui

We characterize all the strongly monotypic polytopes. Hadwiger's conjecture for this class of polytopes is deduced from the characterization.

A short proof of an upper bound on the growth constant of polyiamonds

A characterization of the Carathéodory number for H-convexity

Bounding Klarner's constant from above using a simple recurrence

A characterization of strongly monotypic polytopes

A characterization of the Carathéodory number for $H$ -convexity