Etsuko Bannai

An Upper Bound for the Cardinality of an s -Distance Set in Euclidean Space

In this paper we show that if X is an s-distance set in ℝm and X is on p concentric spheres then

Spin Models on Finite Cyclic Groups

{\left| X \right|} \leqslant {\sum\nolimits_{i = 0}^{2p - 1} {{\left( {\begin{array}{*{20}c} {{m + s - i - 1}} \\ {{s - i}} \\ \end{array} } \right)}} }

New examples of Euclidean tight 4-designs

Moreover if X is antipodal, then

Tight Relative 2- and 4-Designs on Binary Hamming Association Schemes

{\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)}} }

Uniqueness of certain association schemes

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Duality Maps of Finite Abelian Groups and Their Applications to Spin Models

AbstractA spin model is a triple (X, W+, W−), where W+ and W− are complex matrices with rows and columns indexed by X which satisfy certain equations (these equations allow the construction of a link invariant from(X, W+, W−) ). We show that these equations imply the existence of a certain isomorphism Ψ between two algebras