ReadingTableau from IntegerPartition

The recording tableau of the row reading word of the shape filled row by row.

IntegerPartition → StandardTableau

FindStat's Mp00045. Injective. The RSK insertion tableau of that word is the filled shape again, so this is the other half of its pair.

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

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Each element of IntegerPartition 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 IntegerPartition at each size is computed, and compared with the 165 statistics on IntegerPartition: 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 Mp00045

reading tableau

Matched by value: our map agrees with FindStat's image on each of the 29 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

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

Return the RSK recording tableau of the reading word of the (standard) tableau $T$ labeled down (in English convention) each column to the shape of a partition.

Object	Image
[1]	[[1]]
[2]	[[1,2]]
[3]	[[1,2,3]]
[4]	[[1,2,3,4]]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00045 has the rest.