Functional stepped surfaces, flips, and generalized substitutions

Authors:
Pierre Arnoux;Valérie Berthé;Thomas Fernique;Damien Jamet
Affiliations:
IMLCNRS UMR 6206163, Avenue de Luminy, Case 907, 13288 Marseille, Cedex 09, France;LIRMMUMR 5506Univ. Montpellier II, 161 rue Ada, 34392 Montpellier, Cedex 05, France;LIRMMUMR 5506Univ. Montpellier II, 161 rue Ada, 34392 Montpellier, Cedex 05, France;LORIA - Campus Scientifique - BP 239 - 54506 Vandoeuvre-lès-Nancy Cedex, France
Venue:
Theoretical Computer Science
Year:
2007

Citing 9
Cited 8

On the topology of an arithmetic plane.

Theoretical Computer Science
Tilings and rotations on the torus: a two-dimensional generalization of Sturmian sequences

Discrete Mathematics
Automatic Sequences: Theory, Applications, Generalizations

Automatic Sequences: Theory, Applications, Generalizations
Digital straightness: a review

Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Two-dimensional iterated morphisms and discrete planes

Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Digital planarity-A review

Discrete Applied Mathematics
On the language of standard discrete planes and surfaces

IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Discrete surfaces segmentation into discrete planes

IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Bidimensional sturmian sequences and substitutions

DLT'05 Proceedings of the 9th international conference on Developments in Language Theory

Local rule substitutions and stepped surfaces

Theoretical Computer Science
A characterization of flip-accessibility for rhombus tilings of the whole plane

Information and Computation
Generation and recognition of digital planes using multi-dimensional continued fractions

Pattern Recognition
Arithmetic discrete planes are quasicrystals

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Distances on lozenge tilings

DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
About thin arithmetic discrete planes

Theoretical Computer Science
Consistency of multidimensional combinatorial substitutions

Theoretical Computer Science
Fp -affine recurrent n-dimensional sequences over F q are p-automatic

European Journal of Combinatorics

Quantified Score

Hi-index	5.23

Visualization

Abstract

A substitution is a non-erasing morphism of the free monoid. The notion of multidimensional substitution of non-constant length acting on multidimensional words is proved to be well-defined on the set of two-dimensional words related to discrete approximations of irrational planes. Such a multidimensional substitution can be associated with any usual unimodular substitution. The aim of this paper is to extend the domain of definition of such multidimensional substitutions to functional stepped surfaces. One central tool for this extension is the notion of flips acting on tilings by lozenges of the plane.