Back to List of Papers
Welcome to the Hook Formula Homepage!
Hook Length Formulas for Partitions and Plane Trees
GuoNiu Han (Strasbourg)
This web site is devoted to my recent works
on hook length formulas
for partitions and plane trees.
My papers on hook length formulas
[H01] Discovering hook length formulas by an expansion technique, Electronic J. Combinatorics, 15(1), #R133, 2008, 41 pages.
[download   ps  
pdf  ]
[H02] New hook length formulas for binary trees, Combinatorica, 2008, 4 pages.
[download   ps   pdf  ]
[H03] Yet another generalization of Postnikov's hook length formula for binary trees, SIAM J. Discrete Math, 23, 2009, pp. 661664.
[download   ps   pdf  ]
[H04] Some conjectures and open problems on partition hook lengths, Experimental Mathematics, 18, 2009, pp. 97106.
[download   ps   pdf  ]
[H05] The NekrasovOkounkov hook length formula: refinement, elementary proof, extension and applications, Annales de l'Institut Fourier, 2009, 29 pages.
[download   ps   pdf  ]
[H05'] An explicit expansion formula for the
powers of the Euler Product in terms of partition hook lengths,
35 pages, 2008.
[Abstract and Download]
(unpublished,
arXiv:0804.1849 [math.CO])
[H05''] A generalized hook formula for partitions via tcores
and its applications,
13 pages, 2008.
(unpublished, draft version)
[H06] (with Ken Ono) Hook lengths and 3cores, Annals of Combin., 2008, 7 pages.
[download   ps   pdf  ]
[H07] Hook lengths and shifted parts of partitions, The Ramanujan Journal, 2009, 9 pages.
[download   ps   pdf  ]
[H08] (with Ch. Bessenrodt) Symmetry distribution between hook length and part length for partitions, Discrete Mathematics, 309, 2009, pp. 60706073.
[download   ps   pdf  ]
[H09] (with Kathy Q. Ji) Combining hook length formulas and BGranks for partitions via the Littlewood decomposition, Trans. Amer. Math. Soc. 2009, 24 pages.
[download   ps   pdf  ]
Maple programs for verifying the formulas and conjectures
HookExp.mpl 
Document [1]
Last news and comments
[2008.05.01] Laura Yang has generalized hook length formulas for binary trees in [2]
and [3] to kary trees,
arXiv:0805.0109 [math.CO]
[2008.05.04] Mihai Cipu has proved Conjecture 5.2 in [4].
Private communication.
[2008.05.05] Richard Stanley has found an elementary, but not bijective,
proof of the marked hook formula in [4] and [5'].
Private communication.
[2008.05.07] Bruce Sagan has found probabilistic proofs of hook length formulas
for binary trees in [2],
arXiv:0805.0817 [math.CO]
[2008.05.08] Why papers [5'] and [5''] remain
unpublished ?
[2008.05.10] Richard Stanley can prove the k=2 case of Conjecture 3.1 in [4].
Private communication.
[2008.06.18] Richard Stanley proves Conjecture 3.1 in [4].
Private communication.
[2008.07.01] Answer the Quiz.
[2008.07.02] Richard Stanley proved and generalized Conjecture 3.1 in [4]
arXiv:0807.0383 [math.CO]
[2008.07.11] Gil Kalai wrote some comments about my recent works on hook length
formula in his blog,
Powers of Euler Products and Han's Marked Hook Formula
[2008.07.17] Paper [4] is cited by Tewodros Amdeberhan, Differential operators, shifted parts, and hook lengths,
arXiv:0807.2473 [math.CO]
[2008.07.21] Emily Clader, Yvonne Kemper, Matt Wage, Lacunarity of certain
partition theoretic generating functions (arising from Han's generalization
of the NekrasovOkounkov formula) Proceedings of the American Mathematical Society, 137< 2009, pages 29592968.
[2008.07.21]
Ameya Velingker, An exact formula for the coefficients of Han's generating
function Annals of Combinatorics, accepted for publication.
[2008.08.04]
Kevin Carde, Joe Loubert, Aaron Potechin, Adrian Sanborn,
Proof of Han's Hook Expansion Conjecture
D. Collins and S. Wolfe, Congruences for Han's generating function,
Involve, 2 (2009), pages 225236.
G. Panova,
Proof of a conjecture of Okada, arxiv:0811.3463, 2008
W. Y.C. Chen, O. X.Q. Gao and P. L. Guo,
Hook Length Formulas for Trees by Han's Expansion,
Electr. J. Combin.16(1) 2009,
Research Paper R62, 16 pages
Heesung Shin, Jiang Zeng,
An involution for symmetry of hook length and part length of partitions,
to appear in Discrete. Math., 2009, 9 pages
Amitai Regev, Doron Zeilberger,
A MultiSet Identity for Partitions, arXiv:0909.3459v2, 2009, 4 pages
Niklas Eriksen,
Combinatorial proofs for some forest hook length identities, 2009, 5 pages
G. Olshanski,
Plancherel Averages: Remarks on a paper by Stanley, arXiv:0905.1304, 16 pages, 2009
Quiz
Triple mixed hook formula:
What is the numerical value of the following expression ?
0, 1 ,2, 3 or 1001 ?
where t ranges over all binary trees with 1001 vertices,
h_{v}
is the hook length for trees and h_{u} is the hook length
for partitions.
Answer : click here ...
Back to List of Papers 
Send comments to
Email

First version: 2008/04/04

Last update: 2010/01/10