RskInsertion from Permutation

The insertion tableau of the RSK correspondence.

Permutation → StandardTableausurjection

Row insertion with bumping, as a fold over the word whose accumulator is the growing tableau, emitted as its rows. See flat.ts for the indexing rule that makes it evaluate at all.

Called as CombinatorialMap(x, "RskInsertion"). The head's page has its examples.

Live

Explore

Each element of Permutation at a size, and its image, applied in your browser; sizes past 7 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on StandardTableau. Its distribution over the images of Permutation at each size is computed, and compared with the 323 statistics on Permutation: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic RowOfLargestEntryLastEntryInFirstRowLastEntryOnMainDiagonalFirstEntryInLastRowAdjacentSuccessorCountPathLengthToLargestEntryFirstColumnInitialSequenceLengthModularMajorIndexNaturalDescentCountNaturalMajorIndexNaturalComajorIndexChargeCochargeWeightedSizeAttackingPairCountAttackingInversionCountShynarInversionCountAscentCountIncludingLargestEntryShiftedNaturalComajorIndexCylindricalTableauOverlapMinimalCylindricalInnerHeightSmallestCylindricShiftMajorIndexMinusWeightedSizeComajorIndexMinusWeightedSizeHaglundStevensInversionCount Sizes 1 to

FindStat Mp00059

Robinson-Schensted insertion tableau

Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.

Sends a permutation to its Robinson-Schensted insertion tableau.

Object	Image
[1]	[[1]]
[1,2]	[[1,2]]
[2,1]	[[1],[2]]
[1,2,3]	[[1,2,3]]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00059 has the rest.