Reverse from IntegerComposition

The parts read backwards.

IntegerComposition → IntegerCompositioninvolution

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

Live

Explore

Each element of IntegerComposition 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 IntegerComposition. Its distribution over the images of IntegerComposition at each size is computed, and compared with the 44 statistics on IntegerComposition: those that share it are the ones the map sends it to, as far as the sizes computed show.

Statistic LargestPartFirstPartLastPartSmallestPartDistinctPartsLargestMultiplicitySmallestMultiplicityDistinctMultiplicitiesAscentsWeakDescentCountPeaksInversionsCompositionMajorIndexMajorIndexWeakMajorIndexAbsoluteVariationVariationAscentVariationStrongRecordCountWeakRecordCountStrongRecordPositionSumWeakRecordPositionSumLongestWeaklyIncreasingSubsequenceLongestDecreasingSubsequenceLongestStaircaseConstantRunCountLongestConstantRunShortestConstantRunBargraphPeakCountBargraphHalfPerimeterBargraphUpStepCountBargraphValleyHeightSumAsymmetryDegreePartsEqualToReversedPartRotationOrbitSizeStandardImmaculateTableauCountStandardRibbonTableauCountRibbonCornerCountSeaweedIndexDyckPathsAboveBouncePathCountInverseDescentParkingFunctionCountStandardCompositionTableauCountCompositionNakayamaGlobalDimensionDualImmaculateMonomialColumnSum Sizes 1 to

Also from

The same name out of other carriers, each its own implementation: Permutation, SignedPermutation, SetComposition, BinaryWord, ParkingFunction.

FindStat Mp00038

reverse

Matched by value: our map agrees with FindStat's image on each of the 63 rows of size at most 6 we can read (0 unread; its table has 1200 rows).

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

Return the reversal of a composition.

Object	Image
[1]	[1]
[2]	[2]
[3]	[3]
[4]	[4]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00038 has the rest.