Variable Dimension Complexes, Vol. 1: Basic Theory (Classic Reprint) - Couverture souple

Freund, Robert M.

9781333118068: Variable Dimension Complexes, Vol. 1: Basic Theory (Classic Reprint)

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ISBN 10 : 1333118066 ISBN 13 : 9781333118068

Editeur : Forgotten Books, 2018

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�diteur: Forgotten Books
Date d'�dition: 2018
Langue: anglais
ISBN 10: 1333118066
ISBN 13: 9781333118068
Reliure: Broch�
Nombre de pages: 56
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Variable Dimension Complexes, Vol. 1: Basic Theory (Classic Reprint)

Robert M. Freund

Edit� par Forgotten Books, 2016

ISBN 10 : 1333118066 ISBN 13 : 9781333118068

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Vendeur : Forgotten Books, London, Royaume-Uni

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Paperback. Etat : New. Print on Demand. This book introduces Variable-Dimension Complexes (V-Complexes). V-Complexes are employed in the study of combinatorial optimization problems that depend on many parameters. The author restricts their research to finite V-complexes, known as simplicial pivoting algorithms. In Part I of this book, the author establishes the theoretical foundations for V-complexes. In Part II, the author provides constructive, algorithmic proofs of a variety of combinatorial lemmas in topology, including Sperner's lemma, Kuhn's lemma, Scarf's dual Sperner lemma, a generalized Sperner lemma, Tucker's lemma, Gale's hex theorem, and two new dual lemmas on the cube. The relationships between these results, Brouwer's fixed point theorem, the Borsuk-Ulam theorem, and a new set-covering theorem on the simplex are also explored. These results provide valuable insights into the combinatorial nature of variable dimension algorithms and demonstrate their wide applicability in solving problems in a variety of fields, including optimization, game theory, and topology. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N� de r�f. du vendeur 9781333118068_0

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