InforLorV4, Main, Merge, bibRecord, 004B99

Functional Stepped Surfaces, Flips and Generalized Substitutions

Identifieur interne : 004B99 ( Main/Merge ); précédent : 004B98; suivant : 004C00

Functional Stepped Surfaces, Flips and Generalized Substitutions

Auteurs : Pierre Arnoux [France] ; Valerie Berthe [France] ; Thomas Fernique [France] ; Damien Jamet [France]

Source :

Theoretical Computer Science [ 0304-3975 ] ; 2007.

RBID : Hal:lirmm-00180395

English descriptors

mix :
- Arithmetical discrete plane, Dimer tiling, Discrete geometry, Discrete surface, Flip, Generalized substitution, Lozenge tiling, Sturmian word, Word combinatorics.

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.

Url:

http://hal-lirmm.ccsd.cnrs.fr/lirmm-00180395

DOI: 10.1016/j.tcs.2007.03.031

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 002517
to stream Hal, to step Curation: 002517
to stream Hal, to step Checkpoint: 003D58

Links to Exploration step

Hal:lirmm-00180395

Le document en format XML

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<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName>
<orgName type="acronym">UHP</orgName>
<date type="end">2011-12-31</date>
<desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName>
<date type="end">2011-12-31</date>
<desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
<tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName>
<orgName type="acronym">INPL</orgName>
<date type="end">2011-12-31</date>
<desc><address><country key="FR"></country>
</address>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université Nancy 2</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Institut national polytechnique de Lorraine</orgName>
<orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1016/j.tcs.2007.03.031</idno>
<series><title level="j">Theoretical Computer Science</title>
<idno type="ISSN">0304-3975</idno>
<imprint><date type="datePub">2007</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Arithmetical discrete plane</term>
<term>Dimer tiling</term>
<term>Discrete geometry</term>
<term>Discrete surface</term>
<term>Flip</term>
<term>Generalized substitution</term>
<term>Lozenge tiling</term>
<term>Sturmian word</term>
<term>Word combinatorics</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">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.</div>
</front>
</TEI>
</record>

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Functional Stepped Surfaces, Flips and Generalized Substitutions

Functional Stepped Surfaces, Flips and Generalized Substitutions

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