InforLorV4, Main, Exploration, bibRecord, 003B75

Minimal arithmetic thickness connecting discrete planes

Identifieur interne : 003B75 ( Main/Exploration ); précédent : 003B74; suivant : 003B76

Minimal arithmetic thickness connecting discrete planes

Auteurs : Damien Jamet [France] ; Jean-Luc Toutant [France]

Source :

Discrete applied mathematics [ 0166-218X ] ; 2009.

RBID : Pascal:09-0067432

Descripteurs français

Pascal (Inist)
- Arithmétique, Plan, Hyperplan, Calcul 3 dimensions, Vecteur, Algorithme, Géométrie discrète, Connexité, Informatique théorique, Optimisation, Combinatoire, 68Wxx, 52XX.
Wicri :
- topic : Plan.

English descriptors

KwdEn :
- Algorithm, Arithmetics, Combinatorics, Computer theory, Connectedness, Discrete geometry, Hyperplane, Optimization, Plane, Three-dimensional calculations, Vector.
mix :
- Discrete geometry, arithmetic discrete planes, connectedness.

Abstract

While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector n, we provide algorithms either to determine whether a given arithmetic discrete plane with n as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector n is connected.

Url:

https://hal.archives-ouvertes.fr/hal-00579872

Affiliations:

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">Minimal arithmetic thickness connecting discrete planes</title>
<author><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name>
<affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Loria -Univ. Nancy 1, Campus Scientifique, BP 239</s1>
<s2>54506 Vandœuvre-lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>France</country>
<placeName><region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
<settlement type="city">Vandœuvre-lès-Nancy</settlement>
</placeName>
</affiliation>
</author>
<author><name sortKey="Toutant, Jean Luc" sort="Toutant, Jean Luc" uniqKey="Toutant J" first="Jean-Luc" last="Toutant">Jean-Luc Toutant</name>
<affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LIRMM. Univ. Montpellier2, CNRS; 161 rue Ada</s1>
<s2>34392 Montpellier</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</inist:fA14>
<country>France</country>
<placeName><region type="region" nuts="2">Occitanie (région administrative)</region>
<region type="old region" nuts="2">Languedoc-Roussillon</region>
<settlement type="city">Montpellier</settlement>
</placeName>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">INIST</idno>
<idno type="inist">09-0067432</idno>
<date when="2009">2009</date>
<idno type="stanalyst">PASCAL 09-0067432 INIST</idno>
<idno type="RBID">Pascal:09-0067432</idno>
<idno type="wicri:Area/PascalFrancis/Corpus">000284</idno>
<idno type="wicri:Area/PascalFrancis/Curation">000741</idno>
<idno type="wicri:Area/PascalFrancis/Checkpoint">000237</idno>
<idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000237</idno>
<idno type="wicri:doubleKey">0166-218X:2009:Jamet D:minimal:arithmetic:thickness</idno>
<idno type="wicri:Area/Main/Merge">003C71</idno>
<idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-00579872</idno>
<idno type="url">https://hal.archives-ouvertes.fr/hal-00579872</idno>
<idno type="wicri:Area/Hal/Corpus">003183</idno>
<idno type="wicri:Area/Hal/Curation">003183</idno>
<idno type="wicri:Area/Hal/Checkpoint">002F28</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">002F28</idno>
<idno type="wicri:doubleKey">0166-218X:2009:Jamet D:minimal:arithmetic:thickness</idno>
<idno type="wicri:Area/Main/Merge">003839</idno>
<idno type="wicri:Area/Main/Curation">003B75</idno>
<idno type="wicri:Area/Main/Exploration">003B75</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Minimal arithmetic thickness connecting discrete planes</title>
<author><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name>
<affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Loria -Univ. Nancy 1, Campus Scientifique, BP 239</s1>
<s2>54506 Vandœuvre-lès-Nancy</s2>
<s3>FRA</s3>
<sZ>1 aut.</sZ>
</inist:fA14>
<country>France</country>
<placeName><region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
<settlement type="city">Vandœuvre-lès-Nancy</settlement>
</placeName>
</affiliation>
</author>
<author><name sortKey="Toutant, Jean Luc" sort="Toutant, Jean Luc" uniqKey="Toutant J" first="Jean-Luc" last="Toutant">Jean-Luc Toutant</name>
<affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LIRMM. Univ. Montpellier2, CNRS; 161 rue Ada</s1>
<s2>34392 Montpellier</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</inist:fA14>
<country>France</country>
<placeName><region type="region" nuts="2">Occitanie (région administrative)</region>
<region type="old region" nuts="2">Languedoc-Roussillon</region>
<settlement type="city">Montpellier</settlement>
</placeName>
</affiliation>
</author>
</analytic>
<series><title level="j" type="main">Discrete applied mathematics</title>
<title level="j" type="abbreviated">Discrete appl. math.</title>
<idno type="ISSN">0166-218X</idno>
<imprint><date when="2009">2009</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><title level="j" type="main">Discrete applied mathematics</title>
<title level="j" type="abbreviated">Discrete appl. math.</title>
<idno type="ISSN">0166-218X</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithm</term>
<term>Arithmetics</term>
<term>Combinatorics</term>
<term>Computer theory</term>
<term>Connectedness</term>
<term>Discrete geometry</term>
<term>Hyperplane</term>
<term>Optimization</term>
<term>Plane</term>
<term>Three-dimensional calculations</term>
<term>Vector</term>
</keywords>
<keywords scheme="Pascal" xml:lang="fr"><term>Arithmétique</term>
<term>Plan</term>
<term>Hyperplan</term>
<term>Calcul 3 dimensions</term>
<term>Vecteur</term>
<term>Algorithme</term>
<term>Géométrie discrète</term>
<term>Connexité</term>
<term>Informatique théorique</term>
<term>Optimisation</term>
<term>Combinatoire</term>
<term>68Wxx</term>
<term>52XX</term>
</keywords>
<keywords scheme="Wicri" type="topic" xml:lang="fr"><term>Plan</term>
</keywords>
<keywords scheme="mix" xml:lang="en"><term>Discrete geometry</term>
<term>arithmetic discrete planes</term>
<term>connectedness</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the three-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector n, we provide algorithms either to determine whether a given arithmetic discrete plane with n as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector n is connected.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Grand Est</li>
<li>Languedoc-Roussillon</li>
<li>Lorraine (région)</li>
<li>Occitanie (région administrative)</li>
</region>
<settlement><li>Montpellier</li>
<li>Vandœuvre-lès-Nancy</li>
</settlement>
</list>
<tree><country name="France"><region name="Grand Est"><name sortKey="Jamet, Damien" sort="Jamet, Damien" uniqKey="Jamet D" first="Damien" last="Jamet">Damien Jamet</name>
</region>
<name sortKey="Toutant, Jean Luc" sort="Toutant, Jean Luc" uniqKey="Toutant J" first="Jean-Luc" last="Toutant">Jean-Luc Toutant</name>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 003B75 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 003B75 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     Pascal:09-0067432
   |texte=   Minimal arithmetic thickness connecting discrete planes
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

Serveur d'exploration sur la recherche en informatique en Lorraine

Minimal arithmetic thickness connecting discrete planes

Minimal arithmetic thickness connecting discrete planes

Source :

Descripteurs français

English descriptors

Abstract

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

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.