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Duality in Polymatroids and Set Functions

Published online by Cambridge University Press:  12 September 2008

Geoff Whittle
Geoff Whittle
Affiliation:
Mathematics Department, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
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Abstract

Notions of deletion and contraction for the class of set functions from finite sets into the integers are defined. An operation on a subclass of such set functions is a function from the subclass into itself that preserves ground sets and respects isomorphism. The operations on set functions that interchange deletion and contraction are characterised, as are those with the further property of being involutary. Similar results are given for polymatroids. There is a unique involutary operation on the class of k-polymatroids that interchanges deletion and contraction. The results generalise those of Kung [3].

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 275 - 280
Copyright
Copyright © Cambridge University Press 1992

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References

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