Duality in Polymatroids and Set Functions

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].