# Integer Partitions, Tilings of 2D-gons and Lattices

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 36, Issue: 4, page 389-399
- ISSN: 0988-3754

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topLatapy, Matthieu. "Integer Partitions, Tilings of 2D-gons and Lattices." RAIRO - Theoretical Informatics and Applications 36.4 (2010): 389-399. <http://eudml.org/doc/92709>.

@article{Latapy2010,

abstract = {
In this paper, we study two kinds of combinatorial
objects, generalized integer partitions and tilings of 2D-gons
(hexagons, octagons, decagons, etc.).
We show that the sets of partitions,
ordered with a simple dynamics, have the distributive lattice structure.
Likewise, we show that the set of tilings of a 2D-gon
is the disjoint union of distributive
lattices which we describe.
We also discuss the special case of linear integer
partitions, for which other dynamical models exist.
},

author = {Latapy, Matthieu},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Integer partitions; tilings of 2D-gons; lattices; Sand Pile Model discrete
dynamical models.; dynamical models},

language = {eng},

month = {3},

number = {4},

pages = {389-399},

publisher = {EDP Sciences},

title = {Integer Partitions, Tilings of 2D-gons and Lattices},

url = {http://eudml.org/doc/92709},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Latapy, Matthieu

TI - Integer Partitions, Tilings of 2D-gons and Lattices

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 4

SP - 389

EP - 399

AB -
In this paper, we study two kinds of combinatorial
objects, generalized integer partitions and tilings of 2D-gons
(hexagons, octagons, decagons, etc.).
We show that the sets of partitions,
ordered with a simple dynamics, have the distributive lattice structure.
Likewise, we show that the set of tilings of a 2D-gon
is the disjoint union of distributive
lattices which we describe.
We also discuss the special case of linear integer
partitions, for which other dynamical models exist.

LA - eng

KW - Integer partitions; tilings of 2D-gons; lattices; Sand Pile Model discrete
dynamical models.; dynamical models

UR - http://eudml.org/doc/92709

ER -

## References

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- M. Latapy, Generalized integer partitions, tilings of zonotopes and lattices, in Proc. of the 12-th international conference Formal Power Series and Algebraic Combinatorics (FPSAC'00), edited by A.A. Mikhalev, D. Krob and E.V. Mikhalev. Springer (2000) 256-267. Preprint available at http://www.liafa.jussieu.fr/ latapy/
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