Constructions of 1-Perfect Partitions on th n-Cube (Z/2)n

J.Borges, C.Fernandez, J.Rifa & M.Villanueva;

Abstract. We will study 1-perfect partitions, some of their construction and the algebraic structures related to them. We will see the ways if constructing 1-perfect partitions on the n-cube (Z/2)n by using a generalized Slov'eva-Phelps' switching technique. For each 1-perfect distance-preserving partition we can define an associated operation such that Fn becomes distance-compatible quasigroup. We relate the quasigroups associated to isomorphic or equivalent distance-preserving 1-perfect partitions.

Key words: Perfect partitions, switching, distance-preserving, distance-compatible quasigroups.

Registration: PIRDI-1/01, July 2001.

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Copyright © 2001 by Computer Science Department. UAB