ON LATTICES EQUIVALENT TO THEIR DUALS

被引：31

作者：

CONWAY, JH

SLOANE, NJA

机构：

[1] PRINCETON UNIV,DEPT MATH,PRINCETON,NJ 08544

[2] AT&T BELL LABS,MATH SCI RECH INST,MURRAY HILL,NJ 07974

来源：

JOURNAL OF NUMBER THEORY | 1994年 / 48卷 / 03期

关键词：

D O I：

10.1006/jnth.1994.1073

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A lattice is called isodual if it is geometrically congruent to its dual. We show that the densest three-dimensional isodual lattice is the ''mean centered-cuboidal'' lattice, a lattice which is in a sense the mean of the face-centered and body-centered cubic lattices. This lattice is also the most economical three-dimensional isodual covering. We give a number of other dense isodual lattices in R(n), n less-than-or-equal-to 24. (C) 1994 Academic Press, Inc.

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页码：373 / 382

页数：10

相关论文

共 13 条

[1] THE OPTIMAL LATTICE QUANTIZER IN 3 DIMENSIONS [J].

BARNES, ES ;

SLOANE, NJA .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1983, 4 (01) :30-41

[2] A PROBLEM OF DUALITY CONNECTED WITH SPHERES IN THE GEOMETRY OF NUMBERS [J].

BERGE, AM ;

MARTINET, J .

JOURNAL OF NUMBER THEORY, 1989, 32 (01) :14-42

[3]

BUSER P, 1994, INVENT MATH, V117, P24

[4]

Conway J.H., 1985, ATLAS FINITE GROUPS

[5] LOW-DIMENSIONAL LATTICES .6. VORONOI REDUCTION OF 3-DIMENSIONAL LATTICES [J].

CONWAY, JH ;

SLOANE, NJA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1992, 436 (1896) :55-68

[6] LOW-DIMENSIONAL LATTICES .1. QUADRATIC-FORMS OF SMALL DETERMINANT [J].

CONWAY, JH ;

SLOANE, NJA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1988, 418 (1854) :17-41

[7] LOW-DIMENSIONAL LATTICES .2. SUBGROUPS OF GL(N, Z) [J].

CONWAY, JH ;

SLOANE, NJA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1988, 419 (1856) :29-68

[8] FRAGILE LATTICE PACKINGS OF SPHERES IN 3-DIMENSIONAL SPACE [J].

FIELDS, KL .

ACTA CRYSTALLOGRAPHICA SECTION A, 1980, 36 (MAR) :194-197

[9]

KENNEDY GT, DESIGNS FORMALLY SEL

[10] Crystal lattice models based on the close packing of spheres [J].

Patterson, AL .

REVIEW OF SCIENTIFIC INSTRUMENTS, 1941, 12 (04) :206-211