The Cube-A Window to Convex and Discrete GeometryCambridge University Press, 02.02.2006 - 174 Seiten Eight topics about the unit cubes are introduced within this textbook: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular Chuanming Zong demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture. |
Häufige Begriffe und Wortgruppen
A₁ a₂ abelian group algebraic version Assume binary centrally symmetric Clearly combinatorial contains contradicts the assumption convenience convex coordinate counterexample for Keller's cyclic group cyclic sets deduce define det(A det(C Diophantine approximation e₁ easy equivalent Euclidean facets factorization follows Furtwängler's conjecture g₁ g₂ geometry group ring h₁ h₂ Hadamard matrix Hajós induction inequality integer Keller's conjecture lattice tiling Lemma lemma is proved Let G Let H linear logconcave lower bound Math Minkowski's conjecture multiple n-dimensional unit cube Neubauer odd prime orthogonal P₁ positive integer primitive solution problem proceed to show projection Proof of Theorem quotient group relative interior satisfying solution to 7.10 Subcase subgroup of G subset subspace Szabó Theorem 3.7 theorem is proved triangulation u₁ u₂ unit ball unit cube upper bound v₁ v₂ vector vertex vertices write X₁ y₁