On the nomura algebras of formally self-dual association schemes of class $2$

Document Type : Research Paper

Authors

1 Department of Mathematics, K. N. Toosi University of Technology

2 K. N. Toosi university of Technology University, Tehran-Iran.

Abstract

‎‎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.

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References

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.
Transactions on Combinatorics
Volume 2, Issue 3 - Serial Number 3
September 2013
Pages 1-11

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