scholarly journals The Weighted Hook Length Formula III: Shifted Tableaux

10.37236/588 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Matjaž Konvalinka
Keyword(s):  
Simple Proof ◽  
Hook Length ◽  
Bijective Proof ◽  
Branching Rule ◽  
Shifted Tableaux

Recently, a simple proof of the hook length formula was given via the branching rule. In this paper, we extend the results to shifted tableaux. We give a bijective proof of the branching rule for the hook lengths for shifted tableaux; present variants of this rule, including weighted versions; and make the first tentative steps toward a bijective proof of the hook length formula for $d$-complete posets.

scholarly journals A direct bijective proof of the hook-length formula

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Igor Pak ◽  
Alexander V. Stoyanovskii
Keyword(s):  
Young Tableaux ◽  
Hook Length ◽  
Bijective Proof ◽  
International Audience ◽  
Standard Young Tableaux

International audience This paper presents a new proof of the hook-length formula, which computes the number of standard Young tableaux of a given shape. After recalling the basic definitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. The paper concludes with some examples.

scholarly journals A bijective proof of the hook-length formula

1982 ◽  
Vol 3 (4) ◽  
pp. 317-343 ◽  
Author(s):  
D.S Franzblau ◽  
Doron Zeilberger
Keyword(s):  
Hook Length ◽  
Bijective Proof

A Simple Proof of the Hook Length Formula

2004 ◽  
Vol 111 (8) ◽  
pp. 700 ◽  
Author(s):  
Kenneth Glass ◽  
Chi-Keung Ng
Keyword(s):  
Simple Proof ◽  
Hook Length

A bijective proof of the hook-length formula and its analogs

1992 ◽  
Vol 26 (3) ◽  
pp. 216-218 ◽  
Author(s):  
I. M. Pak ◽  
A. V. Stoyanovskii
Keyword(s):  
Hook Length ◽  
Bijective Proof

A Simple Proof of the Hook Length Formula

2004 ◽  
Vol 111 (8) ◽  
pp. 700-704
Author(s):  
Kenneth Glass ◽  
Chi-Keung Ng
Keyword(s):  
Simple Proof ◽  
Hook Length

scholarly journals Symmetry properties of the Novelli-Pak-Stoyanovskii algorithm

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Robin Sulzgruber
Keyword(s):  
Young Tableau ◽  
Sorting Algorithm ◽  
Young Tableaux ◽  
Hook Length ◽  
Jeu De Taquin ◽  
Bijective Proof ◽  
Symmetry Properties ◽  
International Audience ◽  
Standard Young Tableaux ◽  
Standard Young Tableau

International audience The number of standard Young tableaux of a fixed shape is famously given by the hook-length formula due to Frame, Robinson and Thrall. A bijective proof of Novelli, Pak and Stoyanovskii relies on a sorting algorithm akin to jeu-de-taquin which transforms an arbitrary filling of a partition into a standard Young tableau by exchanging adjacent entries. Recently, Krattenthaler and Müller defined the complexity of this algorithm as the average number of performed exchanges, and Neumann and the author proved it fulfils some nice symmetry properties. In this paper we recall and extend the previous results and provide new bijective proofs.

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