19 research outputs found
Some Implications on Amorphic Association Schemes
AMS classifications: 05E30, 05B20;amorphic association scheme;strongly regular graph;(negative) Latin square type;cyclotomic association scheme;strongly regular decomposition
Complex Hadamard matrices contained in a Bose-Mesner algebra
A complex Hadamard matrix is a square matrix H with complex entries of
absolute value 1 satisfying , where stands for the Hermitian
transpose and I is the identity matrix of order . In this paper, we first
determine the image of a certain rational map from the -dimensional complex
projective space to . Applying this result with ,
we give constructions of complex Hadamard matrices, and more generally, type-II
matrices, in the Bose-Mesner algebra of a certain 3-class symmetric association
scheme. In particular, we recover the complex Hadamard matrices of order 15
found by Ada Chan. We compute the Haagerup sets to show inequivalence of
resulting type-II matrices, and determine the Nomura algebras to show that the
resulting matrices are not decomposable into generalized tensor products.Comment: 28 pages + Appendix A + Appendix
Some Implications on Amorphic Association Schemes
AMS classifications: 05E30, 05B20;
Bordered complex Hadamard matrices and strongly regular graphs
We consider bordered complex Hadamard matrices whose core is contained in the
Bose-Mesner algebra of a strongly regular graph. Examples include a complex
Hadamard matrix whose core is contained in the Bose-Mesner algebra of a
conference graph due to J. Wallis, F. Sz\"{o}ll\H{o}si, and a family of
Hadamard matrices given by Singh and Dubey. In this paper, we prove that there
are no other bordered complex Hadamard matrices whose core is contained in the
Bose-Mesner algebra of a strongly regular graph.Comment: 21 pages, corrected typ
Studies on non-amorphous association schemes and spin models
Tohoku University宗政昭弘課