Discovering hook length formulas by expansion technique

2008/05/16 by Guo-Niu Han, Han, Guo-Niu
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.0805.2464

openalex publication_date 2008/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hooks and powers of parts in partitions
• Seiberg-Witten Theory and Random Partitions
• New hook length formulas for binary trees
• Yet another generalization of Postnikov's hook length formula for binary trees

Related

• A note on hook length formulas for trees
• Hook Length Formulas for Trees by Han's Expansion
• New hook length formulas for binary trees
• A multiset hook length formula and some applications
• On the Hook Length Formula for Binary Trees