DeltaMorphism from IntegerComposition

The lengths of the maximal runs of equal parts, left to right.

IntegerComposition → IntegerComposition

FindStat's Mp00133. Lossy: the parts' values are forgotten. RunComposition is the same on a binary word.

Called as CombinatorialMap(x, "DeltaMorphism"). 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

FindStat Mp00133

delta morphism

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).

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

Apply the delta morphism to an integer composition. The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00133 has the rest.