Synopsis
Excerpt from Variable Dimension Complexes, Vol. 1: Basic Theory
Luthi and Kojima and Yamamoto Like other simplicial algorithms, these algorithms usually can be executed with integer or vector labels.
When vector labels are used, it is appropriate to interpret these algorithms as piecewise-linear (pwl) path tracing as in Eaves Kojima and Yamamoto in [9] present a theory of dual pairs of subdivided manifolds that is a basis for interpreting these algorithms via pwl path tracing.
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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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