Geodesic
On Han's hook length formulas for trees
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han's formulas has been generalized to $k$-ary trees by Yang. Sagan has found a probabilistic proof of Yang's extension. We give combinatorial proofs of Yang's formula for $k$-ary trees and the other formula of Han for binary trees. Our bijections are based on the structure of $k$-ary trees associated with staircase labelings.
DOI : 10.37236/642
Classification : 05A19, 05C05
Mots-clés : hook length formula, k-ary tree, combinatorial proof, staircase labeling 
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     author = {William Y.C. Chen and Oliver X.Q. Gao and Peter L. Guo},
     title = {On {Han's} hook length formulas for trees},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/642},
     zbl = {1250.05022},
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William Y.C. Chen; Oliver X.Q. Gao; Peter L. Guo. On Han's hook length formulas for trees. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/642

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