Discrete Geometry and Topology

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PAPERBACK New 082183147X **NEW** Still factory sealed. Book is in excellent condition. No remainder marks. Shipped with delivery confirmation inside US. Selling books since ... 1979*d/BN-R2-113. Read more Show Less

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Brand new. We distribute directly for the publisher. This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests ... centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature. Read more Show Less

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Overview

This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature.

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Editorial Reviews

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Proceedings of the Steklov Institute of Mathematics, volume 196, issue four of four, 1992. Translated from the Russian. Papers discuss the variations of positive quadratic forms, partitioning of Euclidean space into L-polytopes of some perfect lattices, Spanier-Whitehead duality and the stability of the intersection of compacta, curvatures of tangent spheres, geodesic on a Seifert- Weber manifold, three-dimensional spherical forms, the dissociation of point system, and homology on presheaves of sets. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Boris Nikolaevich Delone (on his life and creative work) 1
On variations of positive quadratic forms (with applications to the study of perfect forms) 11
Partitioning of Euclidean space into L-polytopes of some perfect lattices 29
Spanier-Whitehead duality and the stability of the intersection of compacta 53
Combinatorial questions of the two-dimensional Ising model 57
Quadrillages and parametrizations of lattice cycles 73
On mappings of cubic manifolds into the standard lattice of Euclidean space 95
On the curvatures of tangent spheres 99
On a nonregular partitioning of n-dimensional Lobachevsky space by congruent polytopes 103
On a geodesic on a Seifert-Weber manifold 107
Projective Euclidean geometry and noncommutative probability theory 117
Three-dimensional spherical forms 129
On the dissociation of point systems 163
Homology on presheaves of sets 173
Dual systems of integer vectors and their application to the theory of (0,1)-matrices 179
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