• Corpus ID: 232257868

Bijecting hidden symmetries for skew staircase shapes

@inproceedings{Hamaker2021BijectingHS,
  title={Bijecting hidden symmetries for skew staircase shapes},
  author={Zachary Hamaker and Alejandro H. Morales and Igor Pak and Luis G. Serrano and Nathan Williams},
  year={2021}
}
We present a bijection between the set SYT(λ/μ) of standard Young tableaux of staircase minus rectangle shape λ = δk, μ = (b a), and the set ShSYT′(η) of marked shifted standard Young tableaux of a certain shifted shape η = η(k, a, b). Numerically, this result is due to DeWitt (2012). Combined with other known bijections this gives a bijective proof of the product formula for |SYT(λ/μ)|. This resolves an open problem by Morales, Pak and Panova (2019), and allows an efficient random sampling… 
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