RskRecording from Permutation

The recording tableau of the RSK correspondence, as its rows.

Permutation → StandardTableausurjection

Records WHERE each insertion landed: the row the bumped entries end in gets k in its new cell.

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

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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 Mp00070

Robinson-Schensted recording 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 recording 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/Mp00070 has the rest.