Delsarte Method in the Problem on Kissing Numbers in High-Dimensional Spaces

被引：3

作者：

Kuklin, N. A. ^{[1
,2
]}

机构：

[1] Ural Fed Univ, Inst Math & Comp Sci, Ekaterinburg 620000, Russia

[2] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ekaterinburg 620990, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2014年 / 284卷

基金：

俄罗斯基础研究基金会;

关键词：

Delsarte method; infinite-dimensional linear programming; Gegenbauer polynomials; kissing numbers; ALGORITHM; BOUNDS;

D O I：

10.1134/S0081543814020102

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider extremal problems for continuous functions that are nonpositive on a closed interval and can be represented as series in Gegenbauer polynomials with nonnegative coefficients. These problems arise from the Delsarte method of finding an upper bound for the kissing number in a Euclidean space. We develop a general method for solving such problems. Using this method, we reproduce results of previous authors and find a solution in the following 11 new dimensions: 147, 157, 158, 159, 160, 162, 163, 164, 165, 167, and 173. The arising extremal polynomials are of a new type.

引用

页码：S108 / S123

页数：16

共 23 条

[1] Anderson EJ., 1987, Linear Programming in Infinite Dimensional Spaces: Theory and Applications
[2] ARESTOV V. V., 1997, T MAT I STEKLOVA, V219, P36
[3] Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal
Buchberger, B
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 2006, 41 (3-4) : 475 - 511
[4] Conway J. H., 1988, SPHERE PACKINGS LATT, V1
[5] DELSARTE P, 1972, PHILIPS RES REP, V27, P272
[6] Delsarte P., 1973, ALGEBRAIC APPROACH A
[7] Dunford N., 1958, LINEAR OPERATORS GEN
[8] A new efficient algorithm for computing Grobner bases (F4)
Faugére, JC
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 1999, 139 (1-3) : 61 - 88
[9] Kabatyanskii G. A., 1978, Problems of Information Transmission, V14, P1
[10] Kuklin NA, 2011, T I MAT MEKH URO RAN, V17, P225

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