Discovering hook length formulas by expansion technique

Details Discovering hook length formulas by expansion technique Discovering hook length formulas by expansion technique

2008-05-16

arxiv.org/abs/0805.2464v1

Mathematics

Combinatorics

42 pages

Scientific paper

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.

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