The difference matrices of the classes of a Sharma-Kaushik partition

Bhu Dev Sharma and Norris Sookoo

Norris Sookoo
Statistics Department, University of Virginia
Halsey Hall, P.O.  Box 400135, Charlottesville, VA 22904-4135, USA


Sharma-Kaushik partitions have been used to define distances
between vectors with $n$-coordinates. In this paper, ``difference
matrices" for the partitioning classes have been introduced and
investigated. It has been shown that the difference matrices are
circulant and that the entries of a  product of matrices is an
extended intersection number of a  distance scheme.
The sum of the entries of each row or columns of the product
matrix has been obtained.

The algebra  of matrices generated by the difference matrices of
the classes of an SK-partition have another natural basis. The
relationship between these two bases has been given.

AMSclassification. 05A18, 05E99.

Keywords. SK-partitions, distance scheme, extended  intersection number.