On Han's Hook Length Formulas for Trees
Combinatorics
2011-03-22 v1
Abstract
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 with staircase labelings.
Keywords
Cite
@article{arxiv.1103.4068,
title = {On Han's Hook Length Formulas for Trees},
author = {William Y. C. Chen and Oliver X. Q. Gao and Peter L. Guo},
journal= {arXiv preprint arXiv:1103.4068},
year = {2011}
}
Comments
8 pages, 3 figures