notatio

RskShape ​

The common shape of the RSK tableaux: the row lengths, as a partition of n.

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RskShape(Permutation)The common shape of the RSK tableaux: the row lengths, as a partition of n.
Typed signatures
TypePackageApplies
(permutation) -> integer_partitioncombinatoricsalways

Domain: Combinatorial maps

Details
  • Takes a Permutation and returns a IntegerPartition — a typed map, so a wrong carrier is a type error rather than a wrong answer.
  • By Schensted, its first part is the longest increasing subsequence and its first COLUMN is the longest decreasing one — two statistics readable off this map.

Examples

Basic #

the one-line word 231231

live ↗
InRskShape(Permutation⁡([2,3,1]))\mathrm{RskShape}({\operatorname{Permutation}}([2, 3, 1]))OutIntegerPartition⁡([2,1]){\operatorname{IntegerPartition}}([2, 1])
About
Examples1
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