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Linking Structures - On the Combinatorial Structure of Linked Simplices in Straight Line Embeddings of Complete Graphs
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Linking Structures - On the Combinatorial Structure of Linked Simplices in Straight Line Embeddings of Complete Graphs - Livres de poche

2008, ISBN: 9783639063264

[ED: Taschenbuch / Paperback], [PU: VDM Verlag Dr. Müller], As no rings of an iron chain can be separated withoutcutting, no two triangles in 3-space with one edge piercing throughthe interior of the other can be separated by any continuoustransformation without intersecting their boundaries. Thosetriangles are called linked (germ: verschlungen). In graph theoryit is known, that any straight line embedding of the complete graphof 6 vertices in 3-space contains a pair of linked triangles. Usingthe technique of Gale diagrams, we can state this more precisely:either one pair or exactly three pairs of linked triangles exist.Clearing the more general case of pairs of simplices in (d+3)vertices in d-space (d odd) and a linking property of (d+4)vertices lead to the axiomatization of (abstract) linkingstructures including an orientation information, induced by thetopological linking number. These structures are geometricallymotivated but combinatorial objects and emerged from unpublishedconcepts of Prof. U. Brehm (TU-Dresden). Oriented matroids andcomputer-supported proofs allow us to completely classify allgeometrical and oriented-matroid realizable linking structures of6, 7 and 8 points in 3-space as well as 9 points in 5-space., [SC: 0.00], Neuware, gewerbliches Angebot, 22 cm, [GW: 346g]

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Linking Structures - Maik Gerth
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Maik Gerth:
Linking Structures - nouveau livre

ISBN: 9783639063264

ID: 5604eb0aee69f758ff8a8c8950f58b8f

As no rings of an iron chain can be separated withoutcutting, no two triangles in 3-space with one edge piercing throughthe interior of the other can be separated by any continuoustransformation without intersecting their boundaries. Thosetriangles are called linked (germ: verschlungen). In graph theoryit is known, that any straight line embedding of the complete graphof 6 vertices in 3-space contains a pair of linked triangles. Usingthe technique of Gale diagrams, we can state this more precisely:either one pair or exactly three pairs of linked triangles exist.Clearing the more general case of pairs of simplices in (d+3)vertices in d-space (d odd) and a linking property of (d+4)vertices lead to the axiomatization of (abstract) linkingstructures including an orientation information, induced by thetopological linking number. These structures are geometricallymotivated but combinatorial objects and emerged from unpublishedconcepts of Prof. U. Brehm (TU-Dresden). Oriented matroids andcomputer-supported proofs allow us to completely classify allgeometrical and oriented-matroid realizable linking structures of6, 7 and 8 points in 3-space as well as 9 points in 5-space. Bücher / Naturwissenschaften, Medizin, Informatik & Technik / Mathematik, [PU: VDM Verlag Dr. Müller, Saarbrücken]

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Linking Structures - Maik Gerth
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Maik Gerth:
Linking Structures - Livres de poche

2008, ISBN: 9783639063264

[ED: Taschenbuch], [PU: VDM Verlag], Neuware - As no rings of an iron chain can be separated without cutting, no two triangles in 3-space with one edge piercing through the interior of the other can be separated by any continuous transformation without intersecting their boundaries. Those triangles are called linked (germ: verschlungen). In graph theory it is known, that any straight line embedding of the complete graph of 6 vertices in 3-space contains a pair of linked triangles. Using the technique of Gale diagrams, we can state this more precisely: either one pair or exactly three pairs of linked triangles exist. Clearing the more general case of pairs of simplices in (d+3) vertices in d-space (d odd) and a linking property of (d+4) vertices lead to the axiomatization of (abstract) linking structures including an orientation information, induced by the topological linking number. These structures are geometrically motivated but combinatorial objects and emerged from unpublished concepts of Prof. U. Brehm (TU-Dresden). Oriented matroids and computer-supported proofs allow us to completely classify all geometrical and oriented-matroid realizable linking structures of 6, 7 and 8 points in 3-space as well as 9 points in 5-space., [SC: 0.00]

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Linking Structures On the Combinatorial Structure of Linked Simplices in Straight Line Embeddings of Complete Graphs - Gerth, Maik
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Gerth, Maik:
Linking Structures On the Combinatorial Structure of Linked Simplices in Straight Line Embeddings of Complete Graphs - nouveau livre

2008, ISBN: 3639063260

ID: A5997227

Kartoniert / Broschiert, mit Schutzumschlag neu, [PU:VDM Verlag]

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Linking Structures On the Combinatorial Structure of Linked Simplices in Straight Line Embeddings of Complete Graphs - Gerth, Maik
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Gerth, Maik:
Linking Structures On the Combinatorial Structure of Linked Simplices in Straight Line Embeddings of Complete Graphs - nouveau livre

2008, ISBN: 3639063260

ID: A5997227

Leinen, mit Schutzumschlag neu, [PU:VDM Verlag]

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Détails sur le livre
Linking Structures

As no rings of an iron chain can be separated without cutting, no two triangles in 3-space with one edge piercing through the interior of the other can be separated by any continuous transformation without intersecting their boundaries. Those triangles are called linked (germ: verschlungen). In graph theory it is known, that any straight line embedding of the complete graph of 6 vertices in 3-space contains a pair of linked triangles. Using the technique of Gale diagrams, we can state this more precisely: either one pair or exactly three pairs of linked triangles exist. Clearing the more general case of pairs of simplices in (d+3) vertices in d-space (d odd) and a linking property of (d+4) vertices lead to the axiomatization of (abstract) linking structures including an orientation information, induced by the topological linking number. These structures are geometrically motivated but combinatorial objects and emerged from unpublished concepts of Prof. U. Brehm (TU-Dresden). Oriented matroids and computer-supported proofs allow us to completely classify all geometrical and oriented-matroid realizable linking structures of 6, 7 and 8 points in 3-space as well as 9 points in 5-space.

Informations détaillées sur le livre - Linking Structures


EAN (ISBN-13): 9783639063264
ISBN (ISBN-10): 3639063260
Version reliée
Livre de poche
Date de parution: 2008
Editeur: VDM Verlag
252 Pages
Poids: 0,392 kg
Langue: eng/Englisch

Livre dans la base de données depuis 06.07.2009 00:06:55
Livre trouvé récemment le 01.06.2017 14:32:43
ISBN/EAN: 9783639063264

ISBN - Autres types d'écriture:
3-639-06326-0, 978-3-639-06326-4


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