3 citations · 4 across the 13 of their papers we have counts for
13 papers
An optimal refinement-compatible bijection between singleton-free partitions and partitions without cyclic adjacencies
Vuong Bui
It is well known that the number of partitions of without singletons equals the number of partitions of in which no block contains two cyclically adjacent elements $i,i…
A direct injection for the strong -log-convexity of Touchard polynomials
Vuong Bui
We provide a direct injection for the well-known strong log-convexity of the Bell numbers , that is for every . Our injection $Π_m\time…
A sharper log-convexity inequality for Bell numbers
Vuong Bui
We prove a stronger version of the log-convexity inequality for the Bell numbers . In particular, for , we have \[ B_{n+1}B_{n-1} - (B_n)^2 \ge \sum_{i=1}^{n} F_i (B_{…
The mapping index through the lens of the cross-index
Vuong Bui, Hamid Reza Daneshpajouh, Roman Karasev
We study the cross-index of free \(G\)-posets as a combinatorial analogue of the equivariant topological index. We demonstrate that the cross-index exhibits many structural propert…
A convolutional approach to bounding the number of polyominoes
Vuong Bui
Although known lower bounds for the growth rate of polyominoes, or Klarner's constant, are already close to the empirically estimated value , almost no conceptual progres…
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 for the unique real root of the equation . This coincidenta…
A characterization of the Carathéodory number for -convexity
Vuong Bui
We show that the Carathéodory number for -convexity is the maximum of two parameters: the Helly number for -convexity and the cone number of . The cone number in this arti…
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 by viewing polyominoes as a sequence of twig…
Growth of recurrences with mixed multifold convolutions
Vuong Bui
Generalizing some popular sequences like Catalan's number, Schröder's number, etc, we consider the sequence with and for , \begin{multline*} s_n=\sum_{x_1+\do…
Hadwiger's conjecture holds for strongly monotypic polytopes
Vuong Bui
In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.
Every generating polytope is strongly monotypic
Vuong Bui
We prove an old conjecture of McMullen, Schneider and Shephard that every polytope with the generating property is strongly monotypic. The other direction is already known, which i…
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.
On the Carathéodory number for strong convexity
Vuong Bui, Roman Karasev
We give an improvement of the Carathéodory theorem for strong convexity (ball convexity) in , reducing the Carathéodory number to in several cases; and show that t…