In this paper, the type-II matrices on (negative) Latin square graphs are considered and it is proved that, under certain conditions, the Nomura algebras of such type-II matrices are trivial. In addition, we construct type-II matrices on doubly regular tournaments and show that the Nomura algebras of such matrices are also trivial.
E. Bannai and T. Ito (1984). Algebraic combinatorics I. Benjamin Cummings, Menlo Park, California. A. Chan and C. Godsil (2010). Type- II matrices and combinatorial structures. Combinatorica. 30 (1), 1-24 A. Chan and R. Hosoya (2004). Type-II matrices attached to conference graphs. J. Algebraic Combin.. 20 (3), 341-351 P. Delsarte (1973). An algebraic approach to the association schemes of coding theory. Philips Res. Rep. Suppl. No.. 10, 1-97 K. B. Reid and E. Brown (1972). Doubly regular tournaments are equivalent to skew Hadamard matrices. J. Combinatorial Theory Ser. A. 12, 332-338 D. R. Stinson (2004). Combinatorial designs: Constructions and analysis. Spinger-Verlag, New York.
Hosseini, A., & Rahnamai Barghi, A. (2013). On the nomura algebras of formally self-dual association schemes of class $2$. Transactions on Combinatorics, 2(3), 1-11. doi: 10.22108/toc.2013.3002
MLA
Azam Hosseini; Amir Rahnamai Barghi. "On the nomura algebras of formally self-dual association schemes of class $2$". Transactions on Combinatorics, 2, 3, 2013, 1-11. doi: 10.22108/toc.2013.3002
HARVARD
Hosseini, A., Rahnamai Barghi, A. (2013). 'On the nomura algebras of formally self-dual association schemes of class $2$', Transactions on Combinatorics, 2(3), pp. 1-11. doi: 10.22108/toc.2013.3002
VANCOUVER
Hosseini, A., Rahnamai Barghi, A. On the nomura algebras of formally self-dual association schemes of class $2$. Transactions on Combinatorics, 2013; 2(3): 1-11. doi: 10.22108/toc.2013.3002
)