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This paper results from an attempt to unify several different file system design theories. We define a term "partial match pattern" and show that in order to produce file systems optimal with respect to partial match patterns, both the multikey hashing (MKH) method  and the multidimensional directory (MDD) method  must be in such a form that the number of subdivisions is the same for all domains of keys. We show the conditions for the string homomorphism hashing (SHH) method , the MKH method, and the MDD method to be equivalent to one another. We define the so-called Cartesian product files and show that if all records are present, the records in a Cartesian product file form a shortest spanning path in which the Hamming distance between every pair of consecutive records is 1. Thus the SHH method, the MKH method, the MDD method, and the multikey sorting (MKS) method  are linked together. Finally, we show that for both partial and best match queries, the file systems exhibit a common characteristic: similar records are grouped together.