Publications
Papers published on a
journal
Sandpile Models and Lattices: A Comprehensive Survey. E. Goles, M.
Latapy, C. Magnien, M. Movan and H. D. Phan. Theoretical Computer
Science 322 (2004), 383-407.
Lattice
structure and convergence of a Game of Cards Eric Goles, Michel
Morvan and Ha Duong Phan. 1998. Annals of Combinatorics 6 (2002), pp
327-335.
On Overview of Lambda-type Operations on Quasi-symmetric Functions.K.Bertet,
D.Krob, M.Morvan, J.-C. Novelli, H.D.Phan and J.Y.Thibon.
Communications in Algebra 29,9 (2001), pp 4277-4303.
The
Lattice structure of Chip Firing Games M.Latapy and H.D.Phan. 2000.
Physica D 155 (2001), pp 69-82.
Sand
piles and order structure of integer partitions Eric Goles, Michel
Morvan and Ha Duong Phan. Discrete Applied Mathematics 117 (2002), pp
51-64
Structure
of some sand piles models M.Latapy, R.Mantaci, M.Morvan and
H.D.Phan. Theoretical Computer Science 262 (2001), pp 525-556.
The
structure of Linear Chip firing game and related models Eric Goles,
Michel Morvan and Ha Duong Phan. 1998. Theoretical Computer Science 270
(2002), pp 827-841.
An extension of the model of Chip Firing Game. C. Magnien, H. D.
Phan and L. Vuillon. Discrete Math. Theoret.Comput. Sci AA (2001), pp
229-244 .
Papers submitted
Discrete Dynamical System and Unimodal sequences. 14 pages. 2005.
Bidimensional Sand Pile Model. E. Duchi, R. Mantaci, H. D. Phan and D. Rossin. 2005.
Strict partitions and discrete dynamical systems. Le Minh Ha and
Phan Ha Duong. long version, 19 pages. 2004.
The lattice of integer partitions and its infinite extension, long version, M.Latapy and H.D.Phan. 14 pages.
Pseudo-Permutations I: First Combinatorial and Lattice propeties
(long version). Daniel Krob, Matthieu Latapy, Jean-Christophe
Novelli, Ha Duong Phan and Sylvaine Schwer. 2001.
International Conferences (with
lecture commity)
Lattice of integer strict partitions and discrete dynamical
systems. Le Minh Ha and Phan Ha Duong. Journées Montoises,
September 2004, Liège, Belgique.
Strict partitions and discrete dynamical systems. Le Minh Ha and
Phan Ha Duong. 12 pages. FPSAC'04. Juin-July 2004, Vancauver,
Canada.
Dynamics of the Picking transfomation on integer partitions, Ha
Duong Phan et Eric Thierry, Proceedings of the second international
conference DISCRETE MODELS - Combinatorics, Computation and Geometry
(DM-CCG'03), pp 43-56. 2003
Generalized Pseudo-Permutations. Le Minh Ha and Phan Ha Duong.
July 2002. FPSAC. 10 pages.
Pseudo-Permutations
I : First Combinatorial and Lattice properties. Daniel Krob,
Matthieu Latapy, Jean-Christophe Novelli, Ha Duong Phan and Sylvaine
Schwer. November 2000. FPSAC 2001. 12 pages.
About
the Dynamics of Some Systems Based on Integer Partitions and
Compositions Eric Goles, Michel Morvan and Ha Duong Phan. LNCS issue, proceedings
of FPSAC2000. 214-225.
Structure of Chip Firing Game in general. Workshop on Automata.
Ecole Normale supérieure de Lyon. October 1999. Invitée.
The
lattice of integer partitions and its infinite extension M.Latapy
and H.D.Phan. To appear in LNCS
special issue, proceedings of ORDAL'99.
12 pages.
Sand
piles models and discrete ordred structures. Eric Goles, Michel
Morvan and Ha Duong Phan. In International Conference of Combinatorics
and Physics, Los Alamos, New Mexico, August, USA, 1998. 11 pages.
Workshops and seminars
Unimodal sequences and Sand Piles Model. LIAFA, University Paris 7, Juin 2005.
Survey on Discrete dynamical system and Combinatorics. "Pure Mathematics Colloquium", University of Leicester, United Kingdom, PM 05, 05/05/05.
Partitions strictes et système dynamique discret.
Université de La Rochelle, December 2004.
Sandpile Models and Lattices: A Comprehensive Survey.
Université Polytechnique de Hanoi, Viet Nam, avril 2004.
Sandpile Models and Lattices: A Comprehensive
Survey. Institut de Mathématiques, Hanoi, Viet nam, avril
2004.
Partitions strictes. LIAFA, University Paris 7, Octobre 2003.
Pseudo-permutations. 3ème Journées systemes
dynamiques discrets. Sophia-Antipolis & Nice. Mars 2001.
Pseudo-permutations : quelques resultats sur la structure
combinatoire et la structure de treillis. Groupe de travaille DDM
(Discrete Dynamical Models), LIAFA. October 2000.
Chip Firing Game en général et treillis. 2ème
Journées systemes dynamiques discrets. Ecole Polytechnique. May
2000.
La structure du Modele de Piles de sable. Séminaire au
LaBri, Université Bordeaux. November 1999
Modele de Piles de sable et Chip Firing Game. Séminaire au
LIM, Université Marseille. October 1999
Structures ordonnées et dynamiques de piles de sable.
Séminaire groupe de travail de laboratoire LIP, Ecole Normale
Supérieure de Lyon. November 1998
Chip Firing Gmaes. Séminaire du Departamento de
Ingenier\'{\i}a Matem\'atica, Universidad de Chile. April 1998
Santiago, Chili.
Sand Piles Model. Séminaire du STZAKI (Computer and
Automation Institute Hungarian Academy of Sciences, Budapest, Hongrie).
November 1997
Modele de Piles de sable. Groupe de travail du LIAFA. October 1997
Some algorithms for computing plethysms of quasi-symmetric
functions in the sense of Malvenuto and Reutenauer. Séminaire du
Departamento de Ingenier\'{\i}a Matem\'atica, Universidad de Chile,
Santiago, Chili. September 1997
Sand Piles Model. Séminaire du Departamento de
Ingenier\'{\i}a Matem\'atica, Universidad de Chile Santiago, Chili.
August 1997
Structures ordonnes et Modele de Piles de sable. 4ème
Journée sur les ordres, à Paris, (manifestation à
l'audience nationale). May 1997
Structures ordonnes et Modele de Piles de sable. l'école
des
jeunnes chercheurs du PRC/GDR AMI sur le thème ``algorithmique,
modèle et infographie'' à Nice. Décember 1996
Structures ordonnes et Modele de Piles de sable. Séminaire
du LIRMM, à Montpellier. November 1996
Thesis
"Structures
ordonnées et dynamiques de piles de sable", Ph.D. thesis.
111 pages.
*******************************************
"Structures ordonnées et
dynamiques de piles de sable", Ph.D. thesis
LIAFA Technical Report 99/07
Compressed
PostScript file.
On Overview of Lambda-type Operations on
Quasi-symmetric Functions
The Lattice structure of Chip Firing
Games
M.Latapy and H.D.Phan
Abstract :
In this paper, we study a famous discrete dynamical system, the
Chip Firing Game, used as a model in physics, economics and computer
science. We use order theory and show that the set of reachable states
(i.e. the configuration space) of such a system started in any
configuration is a lattice, which implies strong structural properties.
The lattice structure of the configuration space of a dynamical system
is of great interest since it implies convergence (and more) if the
configuration space is finite. If it is infinite, this property implies
another kind of convergence: all the configurations reachable from two
given configurations are reachable from their infimum. In other words,
there is a unique first configuration which is reachable from two given
configurations. Moreover, the Chip Firing Game is a very general model,
and we show how known models can be encoded as Chip Firing Games, and
how some results about them can be deduced from this paper. Finally, we
define a new model, which is a generalization of the Chip Firing Game,
and about which many interesting questions arise.
Keywords : Lattice, Integer partitions,
Dominance ordering, Discrete Dynamical Systems.
About the Dynamics of Some Systems Based
on Integer Partitions and Compositions
Eric Goles - Michel Morvan - Ha Duong Phan
The Lattice of integer partitions and
its
infinite extension
M.Latapy and H.D.Phan
(To appear in LNCS special issue,
proceedings of ORDAL'99.)
LIAFA Technical Report 99/23
Abstract :
In this paper, we use a simple discrete dynamical system to study the
integers partitions and their lattice. The set of the reachable
configurations equiped with the order induced by the transitions of the
system is exactly the lattice of integer partitions equiped with the
dominance ordering. We first explain how this lattice can be
constructed, by showing its strong self-similarity property. Then, we
define a natural extension of the system to infinity. Using a
self-similar tree, we obtain an efficient coding of the obtained
lattice. This approach gives an interesting recursive formula for the
number of partitions of an integer, where no closed formula have ever
been found. It also gives informations on special sets of partitions,
such as length bounded partitions.
Keywords : Lattice, Integer partitions,
Dominance ordering, Discrete Dynamical Systems.
Structure of some sand pile model
M.Latapy, R.Mantaci, M.Morvan and H.D.Phan
Abstract :
SPM (Sand Pile Model) is a simple discrete dynamical system used in
physics to represent granular objects. It is deeply related to integer
partitions, and many other combinatorics problems, such as tilings or
rewriting systems. The evolution of the system started with n stacked
grains generates a lattice, denoted by SPM(n). We study here the
structure of this lattice. We first explain how it can be constructed,
by showing its strong self-similarity property. Then, we define
SPM(infini), a natural extension of SPM when one starts with an
infinite number of grains. Again, we give an efficient construction
algorithm and a coding of this lattice using a self-similar tree. The
two approaches give different recursive formulae for |SPM(n)|, where no
closed formula have ever been found.
Keywords : SPM, Sand Pile Model, Lattice,
Integers partitions, CFG, Discrete Dynamical Systems.
Some algorithms for computing plethysms
of
quasi-symmetric functions in the sense of Malvenuto and Reutenauer
K.Bertet - D.Krob - M.Morvan - H.D.Phan - J.Y.Thibon
Lattice structure and convergence of a
Game of Cards
Eric Goles - Michel Morvan -Ha Duong Phan
Abstract :
We study the dynamics the so-called Game of Cards by using tools
developed in the context of discrete dynamical systems. We extend a
result of Desel and of Huang (this last one in the context of
distributed systems) who stated a necessary and sufficient condition
for the game to converge. We precisely describe the structure of the
set of configurations (that we show to be very closed to a lattice
structure) and we state bounds for the convergence time.
The Structure of a Linear Chip Firing
Game
and related Models
Eric Goles - Michel Morvan -Ha Duong Phan
Sand piles and order structure of integer
partitions
Eric Goles - Michel Morvan - Ha Duong Phan
Abstract :
In this paper, we study the orders obtained by the general ized
dynamics of the Sandpiles Model (SPM). We show that these orders are
sub-lattices of $L_B$, lattice of integer partitions introduced in by
Brylawski, and we deduce from that a characterization of their fixed
point. We prove that these orders form an increasing sequence of
lattices from $SPM$ to $L_B$. We then characterize longest paths in
these lattices and give a formula describing their length.
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