notatio

Rsk ​

The RSK correspondence: the insertion and recording tableaux, as a pair.

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Rsk(Permutation)The RSK correspondence: the insertion and recording tableaux, as a pair.
Typed signatures
TypePackageApplies
(permutation) -> standard_tableau_paircombinatoricsalways

Domain: Combinatorial maps

Details
  • Takes a Permutation and returns a StandardTableauPair — a typed map, so a wrong carrier is a type error rather than a wrong answer.
  • Both tableaux share a shape (RskShape reads it off either), and each carries its own rows, so the pair alone determines them. A standard_tableau_pair is a tuple of two carriers — the first composite carrier anything here constructs.

Examples

Basic #

the one-line word 231231

live ↗
InRsk(Permutation⁡([2,3,1]))\mathrm{Rsk}({\operatorname{Permutation}}([2, 3, 1]))OutStandardTableauPair⁡((StandardTableau⁡([[1,3],[2]]),StandardTableau⁡([[1,2],[3]])))\operatorname{StandardTableauPair}(({\operatorname{StandardTableau}}([[1, 3], [2]]),{\operatorname{StandardTableau}}([[1, 2], [3]])))
About
Examples1
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