InitialTableau from IntegerPartition

The standard tableau of the shape filled row by row with 1, 2, ..., n.

IntegerPartition → StandardTableau

FindStat's Mp00042. Injective.

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

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Explore

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 Mp00042

initial 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.

Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.

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/Mp00042 has the rest.