An Upper Bound for the Cardinality of an <Emphasis Type="Italic">s</Emphasis>-Distance Set in Euclidean 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

按检索

An Upper Bound for the Cardinality of an <Emphasis Type="Italic">s</Emphasis>-Distance Set in Euclidean Space

Authors:	Email author" target="_blank">Etsuko?Bannai Email author Kazuki?Kawasaki Yusuke?Nitamizu Teppei?Sato

Institution:	(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 ^m and X is on p concentric spheres then ${\left\| X \right\|} \leqslant {\sum\nolimits_{i = 0}^{2p - 1} {{\left( {\begin{array}{{20}c} {{m + s - i - 1}} \\ {{s - i}} \\ \end{array} } \right)}} }$ Moreover if X is antipodal, then ${\left\| X \right\|} \leqslant 2{\sum\nolimits_{i = 0}^{p - 1} {{\left( {\begin{array}{{20}c} {{m + s - 2i - 2}} \\ {{m - 1}} \\ \end{array} } \right)}} }$ .

Keywords:	05E99 05B99 51M99 62K99
本文献已被 SpringerLink 等数据库收录！