Synopsis
Explore a rigorous, combinatorial approach to variable-dimension complexes and their applications.
This introduction to the field presents the notion of V-complexes and how labeling drives path-following properties. The work builds a bridge between abstract combinatorial topology and constructive proofs, offering a clear framework for understanding complex pivots, orientability, and related theorems.
This edition guides readers through foundational definitions, key lemmas, and the relationship between V-complexes and H-complexes. It emphasizes algorithmic thinking, with constructive proofs that illuminate how paths on complexes are formed, classified, and oriented. The material lays groundwork for applications in topology and related areas of combinatorial theory.- Definitions and notation for complexes, pseudomanifolds, and orientation
- How labeling induces path-following and the role of end points
- Connections between V-complexes and H-complexes, plus equivalence of path concepts
- Step-by-step orientation procedures and their implications for coherence
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Variable Dimension Complexes, Vol. 1: Basic Theory (Classic Reprint)
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Paperback. Condition: 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. Seller Inventory # 9781333118068_0
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Variable Dimension Complexes, Vol 1 Basic Theory Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333118068
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Variable Dimension Complexes, Vol 1 Basic Theory Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333118068
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