An Upper Bound for the Cardinalityof an <Emphasis Type="Italic">s</Emphasis>-Distance Set inEuclidean Space期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

An Upper Bound for the Cardinalityof an s-Distance Set inEuclidean Space

Authors:	Etsuko?Bannai author-information" > author-information__contact u-icon-before" > mailto:etsuko@math.kyushu-u.ac.jp" title=" etsuko@math.kyushu-u.ac.jp" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Kazuki?Kawasaki,Yusuke?Nitamizu,Teppei?Sato

Affiliation:	(1) Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan;(2) Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan;(3) Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan;(4) Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

Abstract:	In this paper we show that if X is an s-distance set in^mand X is onp concentric spheres then ${left\| X right\|} leqslant {sumnolimits_{i = 0}^{2p - 1} {{left( {begin{array}{{20}c} {{m + s - i - 1}} {{s - i}} end{array} } right)}} }$ Moreover ifX is antipodal, then ${left\| X right\|} leqslant 2{sumnolimits_{i = 0}^{p - 1} {{left( {begin{array}{{20}c} {{m + s - 2i - 2}} {{m - 1}} end{array} } right)}} }$ .

Keywords:	05E99 05B99 51M99 62K99
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