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{\bf Guo-Niu Han}
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{\bf Discovering Hook Length Formulas by an Expansion Technique}
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We introduce a hook length expansion technique and explain how to
discover old and new hook length formulas for partitions and plane
trees. The new hook length formulas for trees obtained by our method
can be proved rather easily, whereas those for partitions are much
more difficult and some of them still remain open conjectures. We also
develop a Maple package {\tt HookExp} for computing the hook length
expansion.  The paper can be seen as a collection of hook length
formulas for partitons and plane trees.  All examples are illustrated
by {\tt HookExp} and, for many easy cases, expained by well-known
combinatorial arguments.



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