AssociatedStandardTableau from SetPartition

The standard tableau whose j-th column holds the j-th smallest elements of the blocks, in increasing order.

SetPartition → StandardTableau

FindStat's Mp00258. Not injective.

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

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Each element of SetPartition 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 SetPartition at each size is computed, and compared with the 111 statistics on SetPartition: 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 Mp00258

Standard tableau associated to a set partition

Matched by value: our map agrees with FindStat's image on each of the 278 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

Surjectionas FindStat records them, checked by FindStat's contributors.

Sends a set partition to the associated standard tableau.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00258 has the rest.