Lionel Nguyen Van Thé
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Lionel Nguyen Van Thé has a total of 3 co-authors. Here are the top co-authors by number of shared publications:
- Norbert Sauer
Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
5 shared publications - Claude Laflamme
University of Calgary
3 shared publications - Vladimir G. Pestov
Departamento de Matemática Universidade Federal de Santa Catarina Trindade 88. 040-900 Florianópolis SC Brazil
1 shared publication
Latest Publications
- Open Access
Some weak indivisibility results in ultrahomogeneous metric spaces
We study the validity of a partition property known as weak indivisibility for the integer and the rational Urysohn metric spaces. We also compare weak indivisiblity to another partition property, called age-indivisibility, and provide an example of a countable ultrahomogeneous metric space which may be age-indivisible but not weakly indivisible.
Open AccessSome weak indivisibility results in ultrahomogeneous metric spaces
We study the validity of a partition property known as weak indivisibility for the integer and the rational Urysohn metric spaces. We also compare weak indivisiblity to another partition property, called age-indivisibility, and provide an example of a countable ultrahomogeneous metric space which may be age-indivisible but not weakly indivisible.
- 19 February 2010
- Published by American Mathematical Society (AMS) in Memoirs of the American Mathematical Society
- Vol. 206 (968)
Structural Ramsey theory of metric spaces and topological dynamics of isometry groups
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore different aspects of this connection.
- 19 February 2010
- Published by American Mathematical Society (AMS) in Memoirs of the American Mathematical Society
- Vol. 206 (968)
Structural Ramsey theory of metric spaces and topological dynamics of isometry groups
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore different aspects of this connection.
- 1 January 2010
- Published by Springer Nature in Combinatorica
- Vol. 30 (1) , 83-104
Partition properties of the dense local order and a colored version of Milliken’s theorem
- 1 January 2010
- Published by Springer Nature in Combinatorica
- Vol. 30 (1) , 83-104
Partition properties of the dense local order and a colored version of Milliken’s theorem
- Open Access
The Urysohn sphere is oscillation stable
We solve the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for the Hilbert space in the context of the Urysohn universal metric space. This is achieved by solving a purely combinatorial problem involving a family of countable homogeneous metric spaces with finitely many distances.
Open AccessThe Urysohn sphere is oscillation stable
We solve the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for the Hilbert space in the context of the Urysohn universal metric space. This is achieved by solving a purely combinatorial problem involving a family of countable homogeneous metric spaces with finitely many distances.
- Open Access
Structural Ramsey theory of metric spaces and topological dynamics of isometry groups
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore the different aspects of this connection.
Open AccessStructural Ramsey theory of metric spaces and topological dynamics of isometry groups
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore the different aspects of this connection.
- Open Access
Fixed point-free isometric actions of topological groups on Banach spaces
We show that every non-precompact topological group admits a fixed point-free continuous action by affine isometries on a suitable Banach space. Thus, precompact groups are defined by the fixed point property for affine isometric actions on Banach spaces. For separable topological groups, in the above statements it is enough to consider affine actions on one particular Banach space: the unique Banach space envelope of the universal Urysohn metric space, known as the Holmes space. At the same time, we show that Polish groups need not admit topologically proper (in particular, free) affine isometric actions on Banach spaces (nor even on complete metric spaces): this is the case for the unitary group of the separable infinite dimensional Hilbert space with strong operator topology, the infinite symmetric group, etc.
Open AccessFixed point-free isometric actions of topological groups on Banach spaces
We show that every non-precompact topological group admits a fixed point-free continuous action by affine isometries on a suitable Banach space. Thus, precompact groups are defined by the fixed point property for affine isometric actions on Banach spaces. For separable topological groups, in the above statements it is enough to consider affine actions on one particular Banach space: the unique Banach space envelope of the universal Urysohn metric space, known as the Holmes space. At the same time, we show that Polish groups need not admit topologically proper (in particular, free) affine isometric actions on Banach spaces (nor even on complete metric spaces): this is the case for the unitary group of the separable infinite dimensional Hilbert space with strong operator topology, the infinite symmetric group, etc.
- Open Access
Partition properties of the dense local order and a colored version of Milliken's theorem
We study the finite dimensional partition properties of the countable homogeneous dense local order. Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of Milliken's theorem on trees.
Open AccessPartition properties of the dense local order and a colored version of Milliken's theorem
We study the finite dimensional partition properties of the countable homogeneous dense local order. Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of Milliken's theorem on trees.
- Open Access
Distinguishing Number of Countable Homogeneous Relational Structures
The distinguishing number of a graph $G$ is the smallest positive integer $r$ such that $G$ has a labeling of its vertices with $r$ labels for which there is no non-trivial automorphism of $G$ preserving these labels. Albertson and Collins computed the distinguishing number for various finite graphs, and Imrich, Klav\v{z}ar and Trofimov computed the distinguishing number of some infinite graphs, showing in particular that the Random Graph has distinguishing number 2. We compute the distinguishing number of various other finite and countable homogeneous structures, including undirected and directed graphs, and posets. We show that this number is in most cases two or infinite, and besides a few exceptions conjecture that this is so for all primitive homogeneous countable structures.Open AccessDistinguishing Number of Countable Homogeneous Relational Structures
The distinguishing number of a graph $G$ is the smallest positive integer $r$ such that $G$ has a labeling of its vertices with $r$ labels for which there is no non-trivial automorphism of $G$ preserving these labels. Albertson and Collins computed the distinguishing number for various finite graphs, and Imrich, Klav\v{z}ar and Trofimov computed the distinguishing number of some infinite graphs, showing in particular that the Random Graph has distinguishing number 2. We compute the distinguishing number of various other finite and countable homogeneous structures, including undirected and directed graphs, and posets. We show that this number is in most cases two or infinite, and besides a few exceptions conjecture that this is so for all primitive homogeneous countable structures.