Catabolism from StandardTableau

Remove the first row and column-insert its entries back into the rest, largest first.

StandardTableau → StandardTableau

FindStat's Mp00106. Not injective: a row and a column of the same size both give the row.

Called as CombinatorialMap(x, "Catabolism"). 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.

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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 Mp00106

catabolism

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).

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

Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.

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/Mp00106 has the rest.