Integer partitions, tilings of 2 D -gons and lattices

Matthieu Latapy

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2002)

  • 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 2 D -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 2 D -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 - Informatique Théorique et Applications 36.4 (2002): 389-399. <http://eudml.org/doc/245645>.

@article{Latapy2002,
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 - Informatique Théorique et Applications},
keywords = {integer partitions; tilings of $2D$-gons; lattices; sand pile model; discrete dynamical models; dynamical models},
language = {eng},
number = {4},
pages = {389-399},
publisher = {EDP-Sciences},
title = {Integer partitions, tilings of $2D$-gons and lattices},
url = {http://eudml.org/doc/245645},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Latapy, Matthieu
TI - Integer partitions, tilings of $2D$-gons and lattices
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2002
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/245645
ER -

References

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  14. [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/ Zbl1168.05007
  15. [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/ Zbl0960.05005
  16. [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/ Zbl0983.68085MR1836234
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