RowDescentsToColumnDescents from StandardTableau

A standard tableau of the same shape whose column descents are the original's row descents.

StandardTableau → StandardTableaubijection

FindStat's Mp00226, a bijection. From the natural labelling of the shape, d and d + 1 are exchanged at each column descent d, the tableau following by the same exchange unless that keeps its descents.

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

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Each element of StandardTableau at a size, and its image, applied in your browser; sizes past 6 are not offered.

Size

Properties

Sizes 1 to

Transport a statistic

Pick a statistic on StandardTableau. Its distribution over the images of StandardTableau at each size is computed, and compared with the 25 statistics on StandardTableau: 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 Mp00226

row-to-column-descents

Matched by value: our map agrees with FindStat's image on each of the 119 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

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

Return a standard tableau whose column descent set equals the row descent set of the original 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/Mp00226 has the rest.