InverseTableauPromotion from StandardTableau

Inverse promotion: replace the entry 1 by n + 1, slide it out to the rim, and subtract one from every entry.

StandardTableau → StandardTableauinverse

FindStat's Mp00153, the inverse of TableauPromotion. The hole is walked through the rows entry by entry, as jeu de taquin does.

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

Live

Explore

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 Mp00153

inverse promotion

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.

The inverse promotion of a standard Young 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/Mp00153 has the rest.