Discovering hook length formulas by an expansion technique 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 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, explained by well-known combinatorial arguments.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Anible, Emily E.; Keith, William J.: Colored partitions and the hooklength formula: partition statistic identities (2020)
  2. Wang, Hua: Note on “hook-length” as a graph invariant of trees (2017)
  3. Kuba, Markus; Panholzer, Alois: Combinatorial families of multilabelled increasing trees and hook-length formulas (2016)
  4. Kuba, Markus; Panholzer, Alois: A unifying approach for proving hook-length formulas for weighted tree families (2013)
  5. Kuba, Markus; Panholzer, Alois: Bilabelled increasing trees and hook-length formulae (2012)
  6. Chen, William Y. C.; Gao, Oliver X. Q.; Guo, Peter L.: On Han’s hook length formulas for trees (2011)
  7. Ciocan-Fontanine, Ionuţ; Konvalinka, Matjaž; Pak, Igor: The weighted hook length formula (2011)
  8. Han, Guo-Niu; Ji, Kathy Q.: Combining hook length formulas and BG-ranks for partitions via the Littlewood decomposition (2011)
  9. Han, Guo-Niu: Hook lengths and shifted parts of partitions (2010)
  10. Han, Guo-Niu: The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications (2010)
  11. Chen, William Y. C.; Gao, Oliver X. Q.; Guo, Peter L.: Hook length formulas for trees by Han’s expansion (2009)
  12. Han, Guo-Niu: Yet another generalization of Postnikov’s hook length formula for binary trees (2009)
  13. Han, Guo-Niu: Some conjectures and open problems on partition hook lengths (2009)
  14. Han, Guo-Niu: Discovering hook length formulas by an expansion technique (2008)