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Hook Length Formulas for Partitions and Plane Trees
Discovering hook length formulas by an expansion technique
By Guo-Niu Han
[download the paper: .ps -
.pdf, 42 pages, 2008/05/08]
Abstract.
We introduce the 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
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 HookExp and, for many easy cases,
expained by well-known combinatorial arguments.
Maple programs for verifing the formulas and conjectures
HookExp.mpl
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Last update: 2008/05/08