On Weakly Eutactic Forms
نویسنده
چکیده
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.
منابع مشابه
On extreme forms in dimension 8
A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension 8 has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for ex...
متن کاملClassification 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 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 کاملOn some forms of e*-irresoluteness
The main goal of this paper is to introduce and study two new class of functions, called weakly $e^*$-irresolute functions and strongly $e^*$-irresolute functions, via the notion of $e^*$-open set defined by Ekici [7]. We obtain several fundamental properties and characterizations of these functions. Moreover, we investigate not only some of their basic properties but also their relat...
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005