Integer Partitions, Tilings of 2D-gons and Lattices

Matthieu Latapy

RAIRO - Theoretical Informatics and Applications (2010)

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

Abstract

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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.

How to cite

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Latapy, 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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  14. M. Latapy and H.D. Phan, The lattice of integer partitions and its infinite extension, in DMTCS, Special Issue, Proc. of ORDAL'99. Preprint (to appear) available at http://www.liafa.jussieu.fr/ latapy/  
  15. 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/  
  16. M. Latapy, R. Mantaci, M. Morvan and Ha Duong Phan, Structure of some sand piles model. Theoret. Comput. Sci.262 (2001) 525-556. Preprint available at http://www.liafa.jussieu.fr/ latapy/  
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