منابع مشابه
Classification of quintic eutactic forms
From the classical Voronoi algorithm, we derive an algorithm to classify quadratic positive definite forms by their minimal vectors; we define some new invariants for a class, for which several conjectures are proposed. Applying the algorithm to dimension 5 we obtain the table of the 136 classes in this dimension, we enumerate the 118 eutactic quintic forms, and we verify the Ash formula.
متن کاملOn Weakly Eutactic Forms
We make precise some properties of the Hermite function in relation with Morse theory introduced by Avner Ash in his papers [Ash1] and [Ash2] and with the cellular decomposition of the space of positive definite quadratic forms. We also establish a link between Ash’s and Bavard’s mass formulae.
متن کاملEutactic quantum codes
The increased experimental feasibility to manipulate single or few particle quantum states, and the theoretical concentration on the algebraic properties of the mathematical models underlying quantum mechanics, have stimulated a wealth of applications in information and computation theory [1,2]. In this line of reasoning, we shall consider quantized systems which are in a coherent superposition...
متن کاملPolyhedral truncations as eutactic transformations.
An eutactic star is a set of N vectors in Rn (N > n) that are projections of N orthogonal vectors in RN. First introduced in the context of regular polytopes, eutactic stars are particularly useful in the field of quasicrystals where a method to generate quasiperiodic tilings is by projecting higher-dimensional lattices. Here are defined the concepts of eutactic transformations (as mappings tha...
متن کاملPerfect, Strongly Eutactic Lattices Are Periodic Extreme
We introduce a parameter space for periodic point sets, given as a union of m translates of a point lattice. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a denser periodic sphere packing. This in particular ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2000
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-00-01295-3