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A Metrization for Power-Sets with Applications to Combinatorial Analysis

Published online by Cambridge University Press:  20 November 2018

Robert Silverman
Robert Silverman*
Affiliation:
Ohio State University and The National Bureau of Standards
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Combinatorial configurations may generally be phrased in terms of arrangements of objects into sets subject to certain conditions. In view of this, the question arises as to whether given a set S and its power-set Us (the class of all subsets of S), it might be possible to structure Us in a combinatorially significant manner. This paper proposes and investigates one such structuring achieved by defining a distance function over US.

Given A, B in Us, define their distance by

where N(E) denotes the number of elements in E, + ∞ being an admissible value.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 158 - 176
Copyright
Copyright © Canadian Mathematical Society 1960

References

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