scholarly journals A crystal-like structure on shifted tableaux

2020 ◽  
Vol 3 (3) ◽  
pp. 693-725
Author(s):  
Maria Gillespie ◽  
Jake Levinson ◽  
Kevin Purbhoo
Keyword(s):  
Shifted Tableaux

scholarly journals Tokuyama's Identity for Factorial Schur $P$ and $Q$ Functions

10.37236/4971 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Angèle M. Hamel ◽  
Ronald C. King
Keyword(s):  
Partition Function ◽  
Lattice Paths ◽  
Schur Function ◽  
Vertex Model ◽  
Shifted Tableaux

A recent paper of Bump, McNamara and Nakasuji introduced a factorial version of Tokuyama's identity, expressing the partition function of  six vertex model as the product of a $t$-deformed Vandermonde and a Schur function. Here we provide an extension of their result by exploiting the language of primed shifted tableaux, with its proof based on the use of non-interesecting lattice paths.

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 Random strict partitions and random shifted tableaux

2020 ◽  
Vol 26 (1) ◽  
Author(s):  
Sho Matsumoto ◽  
Piotr Śniady
Keyword(s):  
Shifted Tableaux

scholarly journals Axioms for Shifted Tableau Crystals

10.37236/8033 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Maria Gillespie ◽  
Jake Levinson
Keyword(s):  
Symmetric Function ◽  
Function Theory ◽  
Type A ◽  
Axiomatic Characterization ◽  
New Method ◽  
Shifted Tableaux

We give local axioms that uniquely characterize the crystal-like structure on shifted tableaux developed by the authors and Purbhoo. These axioms closely resemble those developed by Stembridge for type A tableau crystals. This axiomatic characterization gives rise to a new method for proving and understanding Schur $Q$-positive expansions in symmetric function theory, just as the Stembridge axiomatic structure provides for ordinary Schur positivity.

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