Rank 1 forms, closed zones and laminae

Michel Deza; Viatcheslav Grishukhin

Journal de théorie des nombres de Bordeaux (2002)

  • Volume: 14, Issue: 1, page 103-112
  • ISSN: 1246-7405

Abstract

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For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank 1 quadratic forms which are extreme rays for the corresponding L -type domain.

How to cite

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Deza, Michel, and Grishukhin, Viatcheslav. "Rank $1$ forms, closed zones and laminae." Journal de théorie des nombres de Bordeaux 14.1 (2002): 103-112. <http://eudml.org/doc/93832>.

@article{Deza2002,
abstract = {For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank $1$ quadratic forms which are extreme rays for the corresponding $L$-type domain.},
author = {Deza, Michel, Grishukhin, Viatcheslav},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {quadratic forms; reduction theory; L-type; Delaunay polytopes},
language = {eng},
number = {1},
pages = {103-112},
publisher = {Université Bordeaux I},
title = {Rank $1$ forms, closed zones and laminae},
url = {http://eudml.org/doc/93832},
volume = {14},
year = {2002},
}

TY - JOUR
AU - Deza, Michel
AU - Grishukhin, Viatcheslav
TI - Rank $1$ forms, closed zones and laminae
JO - Journal de théorie des nombres de Bordeaux
PY - 2002
PB - Université Bordeaux I
VL - 14
IS - 1
SP - 103
EP - 112
AB - For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank $1$ quadratic forms which are extreme rays for the corresponding $L$-type domain.
LA - eng
KW - quadratic forms; reduction theory; L-type; Delaunay polytopes
UR - http://eudml.org/doc/93832
ER -

References

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  1. [1] E.P. Baranovskii, V.P. Grishukhin, Non-rigidity degree of a lattice and rigid lattices, European J. Combin.22 (2001), 921-935. Zbl0995.52009MR1857255
  2. [2] B.N. Delaunay (DELONE), Sur la partition régulière de l'espace à 4 dimensions. Izvestia AN SSSR ser. matem.1 (1929), 79-110 et 2 (1929), 145-164. Zbl56.1120.02JFM56.1120.02
  3. [3] P. Engel, Investigations of parallelohedra in Rd. In: P.Engel, H.Syta eds., Voronoi's impact on modern science, Institute of Mathematics, Kyiv1998, vol. 2, 22-60. Zbl0955.51011
  4. [4] R.M. Erdahl, S.S. Ryshkov, On lattice dicing. European J. Combin.15 (1994), 459-481. Zbl0809.52019MR1292957
  5. [5] S.S. Ryshkov, E.P. Baranovskii, C-types of n-dimensional lattices and 5-dimensional primitive parallelohedra (with application to the theory of covering). Trudy of Steklov's Mathematical Institute, vol. 137 (1976), 3-131. (Translated as: Proceedings of Steklov Institute of Mathematics1978, No 4.) Zbl0419.10031
  6. [6] G.F. Voronoi, Nouvelles applications des paramètres continus à la théorie des formes quadratiques - Deuxième mémoire. J. Reine Angew. Math.134 (1908), 198-287 et 136 (1909), 67-178. Zbl38.0261.01JFM39.0274.01

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