European J. Combin., t. 33, p. 227-236, 2012.
Bodo Lass
The Algebra of Set Functions I : The Product Theorem and Duality
Abstract.
We give a comprehensive introduction to the algebra of set functions and its generating functions.
This algebraic tool allows us to formulate and prove a product theorem for the enumeration of
functions of many different kinds, in particular injective functions, surjective functions,
matchings and colourings of the vertices of a hypergraph. Moreover, we develop a
general duality theory for counting functions.
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