scholarly journals The Translative Kissing Number of Tetrahedra Is 18

1999 ◽  
Vol 22 (2) ◽  
pp. 231-248 ◽  
Author(s):  
I. Talata
Keyword(s):  
Kissing Number

scholarly journals The kissing number of the regular polygon

1998 ◽  
Vol 188 (1-3) ◽  
pp. 293-296 ◽  
Author(s):  
Likuan Zhao
Keyword(s):  
Regular Polygon ◽  
Kissing Number

The Kissing Number of the Square

1995 ◽  
Vol 68 (2) ◽  
pp. 128-133
Author(s):  
M. S. Klamkin ◽  
T. Lewis ◽  
A. Liu
Keyword(s):  
Kissing Number

The Kissing Number of the Square

1995 ◽  
Vol 68 (2) ◽  
pp. 128 ◽  
Author(s):  
M. S. Klamkin ◽  
T. Lewis ◽  
A. Liu
Keyword(s):  
Kissing Number

scholarly journals A Combinatorial Approach to Small Ball Inequalities for Sums and Differences

2018 ◽  
Vol 28 (1) ◽  
pp. 100-129 ◽  
Author(s):  
JIANGE LI ◽  
MOKSHAY MADIMAN
Keyword(s):  
Hilbert Spaces ◽  
Vector Spaces ◽  
Combinatorial Approach ◽  
Kissing Number ◽  
Small Ball ◽  
Small Ball Probabilities ◽  
Packing Problems ◽  
Number Problem ◽  
Probabilistic Inequalities ◽  
Independent Identically Distributed

Small ball inequalities have been extensively studied in the setting of Gaussian processes and associated Banach or Hilbert spaces. In this paper, we focus on studying small ball probabilities for sums or differences of independent, identically distributed random elements taking values in very general sets. Depending on the setting – abelian or non-abelian groups, or vector spaces, or Banach spaces – we provide a collection of inequalities relating different small ball probabilities that are sharp in many cases of interest. We prove these distribution-free probabilistic inequalities by showing that underlying them are inequalities of extremal combinatorial nature, related among other things to classical packing problems such as the kissing number problem. Applications are given to moment inequalities.

scholarly journals New formulations for the Kissing Number Problem

2007 ◽  
Vol 155 (14) ◽  
pp. 1837-1841 ◽  
Author(s):  
Sergei Kucherenko ◽  
Pietro Belotti ◽  
Leo Liberti ◽  
Nelson Maculan
Keyword(s):  
Kissing Number ◽  
Number Problem

Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry

2017 ◽  
Vol 27 (3) ◽  
pp. 362-369 ◽  
Author(s):  
Fabrício Caluza Machado ◽  
Fernando Mário de Oliveira Filho
Keyword(s):  
Semidefinite Programming ◽  
Kissing Number
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