BlockSizeComposition from SetComposition

The block sizes of a set composition, its blocks taken in order.

SetComposition → IntegerCompositionsurjection

FindStat's Mp00287. Lossy: which elements share a block is forgotten.

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

Live

Explore

Each element of SetComposition 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 SetComposition at each size is computed, and compared with the 0 statistics on SetComposition: 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: SetPartition.

FindStat Mp00287

to composition

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

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

Return the sizes of the blocks as a composition.

Object	Image
[{1}]	[1]
[{1,2}]	[2]
[{1,2,3}]	[3]
[{1},{2}]	[1,1]

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00287 has the rest.