52B20 — 2 articles found.

Lattice Geometry and Reduction of Finitely Generated Abelian Groups to a Normal Form

C. R. Math. Rep. Acad. Sci. Canada Vol. 36 (4) 2014, pp. 106–113
Vol.36 (4) 2014
Leonid Monin Details
(Received: 2014-04-02 , Revised: 2014-08-13 )
(Received: 2014-04-02 , Revised: 2014-08-13 )

Leonid Monin, Department of Mathematics, University of Toronto, Toronto, ON Canada M5S 2E4 e-mail: lmonin@math.toronto.edu

Abstract/Résumé:

In this paper the geometry of the lattice is used to prove basic theorems about subgroups and factor groups of \(\Bbb Z^n\). We suggest a geometric algorithm which reduces a finitely generated abelian group to its normal form.

Dans ce papier, un argument de géométrie sur les réseaux est utilisé pour prouver des théorèmes fondamentaux sur les sous-groupes ou les groupes quotients de \(\Bbb Z^n\). Nous proposons un algorithme géométrique qui réduit un groupe abélien finement engendré à sa forme normale.

Keywords: Integer lattice, Integer volume, Normal Smith form

AMS Subject Classification: Lattice polytopes (including relations with commutative algebra and algebraic geometry) 52B20

PDF(click to download): Lattice Geometry and Reduction of Finitely Generated Abelian Groups to a Normal Form

Space filling zonotopes and Voronoi’s conjecture on parallelohedra

C. R. Math. Rep. Acad. Sci. Canada Vol. 20 (1) 1998, pp. 2–15
Vol.20 (1) 1998
R.M. Erdahl Details
(Received: 1997-12-01 )
(Received: 1997-12-01 )

R.M. Erdahl

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Quadratic forms (reduction theory; extreme forms; etc.), Lattice polytopes (including relations with commutative algebra and algebraic geometry), , Tilings in $n$ dimensions 11H55, 52B20, 52B30, 52C22

PDF(click to download): Space filling zonotopes and Voronoi's conjecture on parallelohedra

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