KnuthClassRepresentative

The row reading word of σ's RSK insertion tableau — the canonical word of its Knuth (plactic) class.

KnuthClassRepresentative(Permutation)The row reading word of σ's RSK insertion tableau — the canonical word of its Knuth (plactic) class.

Typed signatures

Type	Package	Applies
(permutation) -> permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a Permutation and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Two permutations are Knuth-equivalent exactly when they share an insertion tableau (Schensted), so reading that tableau back out — bottom row to top, left to right — picks one fixed representative per class. Idempotent: the representative's own insertion tableau is the same P, so applying this again changes nothing.

Examples

Basic #

the one-line word $231$

live ↗

In$\mathrm{KnuthClassRepresentative}({\operatorname{Permutation}}([2, 3, 1]))$Out${\operatorname{Permutation}}([2, 1, 3])$

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Examples	1