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In order to prepare the applications of this lemma and its refinements which follow in the next chapters, a detailed description of the conjugacy classes of symmetric and of monomial groups is added.

The
paradigmatic actions
which
we discuss and apply in full detail here and later on are several natural
actions on the set *Y ^{X}*,
consisting of all the mappings from

The enumeration of symmetry classes of mappings is described in full detail, in order to prepare refinements which are given in the following chapters.

A very simple case of a group action leads to another important enumerative concept, the so-called involution principle. Finally we discuss the enumeration of symmetry classes which consist of injective or surjective mappings only.

harald.fripertinger@kfunigraz.ac.at,

last changed: August 28, 2001

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