CyclicShift from IntegerComposition

Rotate the parts one place to the left: the first part moves to the end.

IntegerComposition → IntegerCompositioninverse

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

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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, SetComposition, BinaryWord, ParkingFunction.

FindStat Mp00173

rotate front to back

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

The front to back rotation of the entries of an integer composition.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00173 has the rest.